novel techniques for quasi three-dimensional nanofabrication of transformation optics devices
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Open Access Dissertations Theses and Dissertations
Winter 2015
Novel techniques for quasi three-dimensionalnanofabrication of Transformation Optics devicesPaul R. WestPurdue University
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Recommended CitationWest, Paul R., "Novel techniques for quasi three-dimensional nanofabrication of Transformation Optics devices" (2015). Open AccessDissertations. 591.https://docs.lib.purdue.edu/open_access_dissertations/591
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PURDUE UNIVERSITY GRADUATE SCHOOL
Thesis/Dissertation Acceptance
Department
Paul R. West
NOVEL TECHNIQUES FOR QUASI THREE-DIMENSIONAL NANOFABRICATION OF TRANSFORMATION OPTICS DEVICES
Doctor of Philosophy
Alexandra Boltasseva Vladimir Shalaev
Alexander Kildishev Minghao Qi
Xianfan Xu
Alexandra Boltasseva
Venkataramanan Balakrishnan 01/15/2015
To the best of my knowledge and as understood by the student in the Thesis/Dissertation Agreement, Publication Delay, and Certification/Disclaimer (Graduate School Form 32), this thesis/dissertation adheres to the provisions of Purdue University’s “Policy on Integrity in Research” and the use of copyrighted material.
NOVEL TECHNIQUES
FOR
QUASI THREE-DIMENSIONAL NANOFABRICATION
OF
TRANSFORMATION OPTICS DEVICES
A Dissertation
Submitted to the Faculty
of
Purdue University
by
Paul R. West
In Partial Fulfillment of the
Requirements for the Degree
of
Doctor of Philosophy
May 2015
Purdue University
West Lafayette, Indiana
ii
I dedicate this thesis to my parents, Rob and Jan, for providing their support, and
every opportunity for my education.
iii
ACKNOWLEDGMENTS
I would like to start by acknowledging some of the people, without who none of
this work would have been possible.
Sasha, six years ago we both came to Purdue with empty lab space and empty
offices. It’s amazing to look back on how far we have come in just the last few years,
and it makes me proud to have been a part of our research group. Thank you for
giving me the freedom to explore my ideas and chase my curiosities in research. Your
kindness and encouraging presence helped me through graduate schools most grueling
days. Thank you for giving me the opportunity to help teach your classes and summer
programs. I learned so much more than science and research in graduate school, and
I owe so much of that to you.
Vlad, you pushed us to focus on the grand challenges, the breakthroughs that
would make a difference. I could work hard with the knowledge that our projects
would have a huge impact in the field - looking back on it, you were absolutely right!
You also taught us that there is a human aspect of our research the relationships
between people are worth even more. You helped me realize I could do more than I
thought I was capable of, and my respect for you made me want to live up to your
expectations.
Alex, when I was looking back through the slides for my final defense, I realized
that your impact could be seen on nearly every slide. Whether it was an idea you
had, a simulation you taught me to do, or just giving me feedback on my presentation
your help was so important to my work, and I really dont know how I could have
done it without you. Your courage and perseverance inspired me to fight on and keep
working, even when times were tough. When I would be struggling with a difficult
problem, it was always such a relief when you would come by the office to ask how
research was going, or just how I was doing. Not every graduate student has a mentor
iv
who not only helps, but really cares about their students, and I am so glad to have
had someone like you.
I would like to thank my family, for providing me the support, and opportunities
I needed to succeed. My parents, who pushed me to always do my best and kept me
in school. My three sisters: Erin, Elaine, and Adrienne - it’s not easy following in the
footsteps of three such successful siblings, but I’m trying to keep up!
Natalie van Hoose, thank you for all your patience, help, and support during
our time at Purdue - I couldn’t have done it without you. Most of all, thank you
for teaching me to see with a new light, challenging me to think in new ways, and
showing me how to become a better person.
Finally, I would like to thank all of my past and present group members with
whom I spent the majority of my last six years. I learned so much from every one
of you. Not only did you help me with research topics, but you provided a great
environment in which to thrive. Outside of work, I have developed close friendships
with many of you. Thank you for being there for me - you have been my home away
from home while at Purdue.
v
TABLE OF CONTENTS
Page
LIST OF TABLES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . x
SYMBOLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii
ABBREVIATIONS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xviii
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xx
1 PLASMONIC MATERIALS - CHALLENGES AND APPROACHES . . 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Survey of Alternative Plasmonic Materials . . . . . . . . . . . . . . 7
1.3.1 Metals as Candidates for Plasmonics . . . . . . . . . . . . . 8
1.3.2 Metallic Alloys . . . . . . . . . . . . . . . . . . . . . . . . . 11
1.3.3 Semiconductors . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3.4 Graphene . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
1.4 Quality Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
1.5 Comparative Studies . . . . . . . . . . . . . . . . . . . . . . . . . . 23
1.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2 NANOWIRES GROWNWITHGLANCING ANGLE DEPOSITION (GLAD) 27
2.1 Comparing Traditional PVD to GLAD . . . . . . . . . . . . . . . . 27
2.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.3 Random Nanolasing . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.4 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.5 Advanced Nanowire Growth Techniques . . . . . . . . . . . . . . . 33
2.6 Nanowires Grown on a Seeded Template . . . . . . . . . . . . . . . 35
2.7 Complex Nanowires from Previous Literature . . . . . . . . . . . . 36
vi
Page
3 GLANCING ANGLE DEPOSITION ON CURVED AND SPHERICAL SUR-FACES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
3.2 Angled Deposition on Curved Surfaces . . . . . . . . . . . . . . . . 38
3.3 Comments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4 SHADOWEDANGLED DEPOSITION FOR THICKNESS TAPERED THINFILM HYPERBOLIC HYPERBOLIC METAMATERIALS AND WAVEG-UIDES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.2 Tapered Silver Films on Uniform SiO2 . . . . . . . . . . . . . . . . 45
4.3 Tapered SiO2 films on Uniform Silver . . . . . . . . . . . . . . . . . 47
4.4 Planar Magnifying Hyperlens . . . . . . . . . . . . . . . . . . . . . 49
4.5 Design and Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . 49
4.6 Simulations and Remarks . . . . . . . . . . . . . . . . . . . . . . . 50
5 INTRODUCTION TO HYPERBOLIC METAMATERIALS . . . . . . . 52
6 TAPERED HYPBERBOLIC METAMATERIAL WAVEGUIDES . . . . 56
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
6.2 Outcoupling High-k Waves from HMMs . . . . . . . . . . . . . . . . 56
6.3 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
6.4 Simulations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
6.5 Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
6.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
7 ALL-DIELECTRIC FULL-PHASE CONTROLLED METASURFACES . 67
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
7.2 Detailed Description . . . . . . . . . . . . . . . . . . . . . . . . . . 68
7.3 Anomalous Refraction with Dielectric Metasurfaces . . . . . . . . . 72
8 ALL-DIELECTRIC METASURFACE FOCUSING LENS . . . . . . . . . 78
8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
8.2 Approach . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
vii
Page
8.3 Design . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
8.4 Fabrication Method . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
8.5 Phase Increment Measurement . . . . . . . . . . . . . . . . . . . . . 85
8.6 Focusing Effect . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
8.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
9 STUDIES OF METAL/DIELECTRIC COMPOSITE SUPERLENS . . . 93
9.1 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
9.2 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
9.2.1 Nanoantenna Pattern Design and Fabrication . . . . . . . . 98
9.2.2 Superlens Design . . . . . . . . . . . . . . . . . . . . . . . . 99
9.2.3 Sample Characterization . . . . . . . . . . . . . . . . . . . . 100
9.2.4 Far-Field Characterization . . . . . . . . . . . . . . . . . . . 102
9.2.5 Near-Field Characterization . . . . . . . . . . . . . . . . . . 103
9.3 Bare Antennas . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
9.4 Superlens and Reference Samples . . . . . . . . . . . . . . . . . . . 107
9.5 FDTD Simulations for Far-Field Spectra and Near-field Intensity Mapsof the Superlens and Reference Samples . . . . . . . . . . . . . . . . 110
9.5.1 Representative FDTD Near-Field Intensity Maps for Bare An-tenna Sample . . . . . . . . . . . . . . . . . . . . . . . . . . 113
9.6 Comparing FDTD Simulations to NSOM . . . . . . . . . . . . . . . 113
9.6.1 Bare Antenna Sample . . . . . . . . . . . . . . . . . . . . . 114
9.6.2 Superlens Sample . . . . . . . . . . . . . . . . . . . . . . . . 114
9.6.3 Reference Sample . . . . . . . . . . . . . . . . . . . . . . . . 115
9.7 Conclusions and Final Remarks . . . . . . . . . . . . . . . . . . . . 116
LIST OF REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
A ELECTROMAGNETIC BOUNDARY CONDITIONS FOR NANOMETER-SCALE CONFINEMENT AT METAL-DIELECTRIC INTERFACES . . 135
A.1 Multilayer Systems and Plasmonic Waveguides . . . . . . . . . . . . 138
A.2 Localized Surface Plasmon Resonance and Nano-Antennas . . . . . 140
viii
Page
A.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
B GLANCING ANGLE DEPOSITION (GLAD) - NOVEL APPROACH FORQUASI 3D FABRICATION . . . . . . . . . . . . . . . . . . . . . . . . . 143
B.1 Glancing Angle Deposition at Purdue . . . . . . . . . . . . . . . . . 143
B.1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
B.1.2 Hardware . . . . . . . . . . . . . . . . . . . . . . . . . . . . 143
B.1.3 Automation and Computer User Interface . . . . . . . . . . 146
B.1.4 WORDS OF CAUTION . . . . . . . . . . . . . . . . . . . . 147
C STEP-BY-STEP INSTRUCTIONS FOR OPERATING GLAD . . . . . . 149
C.1 Loading and Unloading the GLAD Chamber . . . . . . . . . . . . . 149
C.2 Running an Evaporation . . . . . . . . . . . . . . . . . . . . . . . . 150
C.3 Other Notes and Comments . . . . . . . . . . . . . . . . . . . . . . 151
VITA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152
ix
LIST OF TABLES
Table Page
1.1 Drude model parameters for metals. ωint is the frequency of onset forinterband transitions. Drude parameters tabulated are not valid beyondthis frequency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2 Table comparing various plasmonic metals researched in this study . . 24
8.1 Lens Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
x
LIST OF FIGURES
Figure Page
1.1 The losses in Cu shown as the sum of interband losses and free electronlosses [39, 59]. Annotations identify the interband transitions responsiblefor peaks in ε′′ . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2 Real (a) and imaginary (b) parts of the permittivities of Ag, Au, Na, K,and Al. The data for Ag, and Au are taken from [39], and those of Al,Na, and K are from [78] . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3 By courtesy of Dr. M. Noginov and Dr. V. Gavrilenko, Norfolk University[106]) Numerical simulation detailing the shift in interband transition peakand modified band structure when Au [39] is doped with 3.3 at.% Cd.The dashed curve shows the imaginary permittivity for the undoped gold,while the solid curve is the result for the doped alloy. The doping processcombines the losses from peaks I & II into a single, confined high-lossregion, while leaving lower losses elsewhere. . . . . . . . . . . . . . . . 13
1.4 Real (a) and imaginary (b) parts of permittivity of ITO annealed at variousconditions (N2, 450
◦C; N2, 650◦C; O2, 450◦C; O2, 650
◦C). . . . . . . . 17
1.5 Real (a) and imaginary (b) parts of permittivity of AZO and GZO ob-tained from parameters reported in reference [125]. The losses in AZOand GZO are much smaller than that of silver [39] at the telecommunica-tion wavelength. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
1.6 Quality factors for localized surface plasmon resonances (QLSPR) is shownin panel (a), and surface plasmon polaritons quality factor (QSPP ) is shownin panel (b). The permittivity values used to calculate the presentedquality factors are the same as those shown in Fig. 1.2 . . . . . . . . . 21
2.1 Growth mechanism for nanowire growth using GLAD. The red arrows rep-resent silver deposited at an oblique angle to the substrate. The red ellipsesrepresent actively growing nanowires, while the gray ellipses represent thenanowires that have been shadowed and are no longer growing. . . . . 29
2.2 Side and top views of the randomly grown array of Ag nanowires . . . 30
2.3 Three nanowire samples grown by GLAD with three effective depositionthicknesses (400nm, 700nm, 1μm). . . . . . . . . . . . . . . . . . . . . 32
2.4 The setup for nanolasing optical measurements . . . . . . . . . . . . . 33
xi
Figure Page
2.5 a) The intensity spectrum for the 3 nanowire samples compared to a blankglass sample. b) The output intensity as a function of the input pumpingpower. Both curves show characteristic behavior for lasing . . . . . . . 34
2.6 “Chevron nanowire - grown by rotating the sample 180◦ in the middle ofthe deposition. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.7 Silver chiral structures with 90◦ counter-clockwise rotation grown on aZnO nanowire template . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.8 Silver nanowires grown from a seeded template. As the nanowires onlygrow from the seeded template, their size is more uniform in size, shape,and length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.9 Various types of nanowire growth via GLAD techniques . . . . . . . . . 37
3.1 Schematic of angled PVD deposition on a spherical surface. A gradient inthickness is created due to the varying amounts of surface exposed at theangle of deposition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2 A 40nm silver deposited at a 45◦ angle over a 5μm SiO2 microsphere. Adistribution in effective thickness can be seen ranging from no coveragethrough full continuous coverage. . . . . . . . . . . . . . . . . . . . . . 40
3.3 Deposition of silver on SiO2 microsphere without germanium wetting layer.Despite the films’ relatively large thicknesses, layers are rough and discon-tinuous. The top of the structure is especially rough, due to the shadowed,“nanowire”-like growth of the films at sharp glancing angles . . . . . . 41
3.4 1μm SiO2 microsphere before (a) and after (b) FIB cut. Although layersare only ∼13nm each, they remain relatively smooth and continuous . . 42
3.5 Gradient film thicknesses around a 5μm microsphere. Fig.3.5a shows theentire microsphere, while Fig.3.5b is an inset of the sphere, showing thedifference in film thicknesses between the top and sides of the sphere. . 43
4.1 Depositing material at an angle over a mask will produce a shadowedregion behind the mask with a tapered deposition thickness profile. . . 46
4.2 Alternating metal / dielectric layers with subwavelength thickness . . . 47
4.3 15 alternating silver/SiO2 layers. Each silver layer has a uniform thicknessof 10nm. Each SiO2 layer has a thickness that tapers between 30nm and100nm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
4.4 Simulations used to calculate the magnification induced from the HMMwedge structure. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
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Figure Page
5.1 Alternating metal / dielectric layers with subwavelength thickness andcoordinate system used. . . . . . . . . . . . . . . . . . . . . . . . . . . 52
5.2 Dispersion relations for air, SiO2, and an HMM structure, demonstratinghow waves propagating in the z-direction cannot be coupled to air or SiO2
because the y-components of the wave vectors cannot be matched. . . . 53
6.1 Dispersion relations for various dielectric and HMM structures. Fig. (a)demonstrates how waves propagating in the z-direction cannot be coupledto air or SiO2. Waves propagating along the y-axis can be coupled toSiO2 or air, as they have matching z-components of their respective wave-vectors. Fig. (b) shows how the dispersion relation for various dielectricand HMMs change as a function of metallic filling fraction. . . . . . . . 59
6.2 Outcoupling of enhance emission of single-photon emitters . . . . . . . 61
6.3 Quenching of high-k waves passing through metamaterial with decreasingmetallic filling fraction . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
6.4 Outcoupling efficiencies of HMMs with various metal filling fractions (a).Simulated outcoupling for one of the more high-efficient modes (b). . . 63
6.5 Outcoupling of enhance emission of single-photon emitters . . . . . . . 64
6.6 Outcoupling of enhanced emission of single-photon emitters . . . . . . 65
7.1 The figure on the left shows an abrupt change in height, resulting in a 2πphase shift. The figure on the right shows a gradient transition from nlow
to nhigh, providing any phase between 0 and 2π . . . . . . . . . . . . . 69
7.2 Periodic arrays of 4 different dielectric metasurface element types (a) LargePosts, (b) Small Posts, (c) Large Holes, (d) Small Holes. Each elementtype has a corresponding phase accumulation associated with it. In gen-eral, the phase shift corresponds with the filling fraction of high-index tolow index materials in the structures. Generally, (a) - (d) correspondswith the phase accumulation from least to greatest. In addition to these4 structures, purely low-index, or purely high-index elements can be im-plemented - corresponding with smallest and largest phase displacement(respectively). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
7.3 Phase displacement corresponding with various post / hole structures.Posts and holes on the bottom are schematic sketches of holes and postsof different sizes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
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Figure Page
7.4 Extraordinary refraction arising from the distribution in phase accumu-lation along the dielectric metasurface. The top figure shows one unitcell of the extraordinary reflection / refraction array. The bottom figureshows a beam entering a metasurface and undergoing extraordinary reflec-tion or refraction. A similar approach can be taken for reflecting light atextraordinary angles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
7.5 Schematic showing the major steps of the fabrication process. . . . . . 74
7.6 Sideview of the post and hole structures fabricated for anomalous refrac-tion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
7.7 Angular transmission measurements at λ = 1.55μm. . . . . . . . . . . . 76
7.8 Spectroscopic angular scan of the transmission through the silicon meta-surface for p-polarization (Results are almost identical for s-polarization). 77
8.1 Plane wave-fronts (shown in red) travelling through a conventional thick,curved lens (a), compared to a thick gradient index (GRIN) lens (b), andto a thin, flat meta-surface lens (c). . . . . . . . . . . . . . . . . . . . . 82
8.2 Top-view of the two realizations of the lens designs: a square lens (left),and the rounded lens (right), with notched belt corners. The colored regionshows the arrangement of the belts for each lens. . . . . . . . . . . . . 83
8.3 Schematic showing the major steps of the fabrication process. . . . . . 84
8.4 Side-view of the pillar structures that modulate the phase of light passingthrough the lens. Pillars of large and small diameter etched to similardepths. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
8.5 Experimental setup for optical phase measurements. The phase of eachuniform array was measured by detecting the lateral shift in the inter-ference pattern created between the beam passing through the patternedsurface and the bare silicon surface. . . . . . . . . . . . . . . . . . . . . 86
8.6 Simulation (blue) and experimental measurements (red) for phase incre-ments added by patterned meta-surfaces for the 15 pillar structures. Theblack error bars represent the 15% margin of error in the experimentalmeasurements. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
8.7 Schematic of the focusing effect demonstration. The single mode radiationfrom an Er fiber laser was tightly focused on the Si sample surface tomonitor beam diffraction behind the surface micro-lens using a simpleimaging system. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
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Figure Page
8.8 Intensity profiles taken at different image planes behind the micro-lenssurface measured from the input surface of the wafer. The micro-lensis strong enough to focus light inside the wafer. The yellow-color framedepicts a 30μm x 30μm box equivalent to the size of the micro-lens. . . 89
8.9 The light intensity distribution at the micro-lens surface (a), at the min-imal spot size focusing plane (b), and at two focal lengths behind thefocusing plane (c). The yellow frame depicts a 30μm × 30μm square rep-resenting the size of the original lens. Secondary reflection spots are visiblenear left lower corner of the photos. The intensity of the Gaussian beamat the micro-lens input (green) is compared to the measured intensity atthe focusing plane (blue) for one of the micro-lenses (d). This particularmicro-lens increased the axial intensity by a factor of 1.87. . . . . . . . 91
9.1 Schematic of a lamellar, alternating multilayer metal-dielectric system(left). The metal is white, the dielectric is gray, and the layers are sub-wavelength in thickness. This scheme provides a method of adjustingthe operational wavelength of a superlens. A cross-section SEM view ofa silver- silica prototype superlens design with layer thicknesses labeled(right). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
9.2 Schematics of the basic nanoantenna design. (a) A nanoantenna pair in topview and cross section. Two 40nm thick rhombus-shaped antennas forma single pair and are spaced 20nm apart. The antenna pair is embeddedinto a quartz substrate. (b) The individual antenna pairs are part of largerarrays. The size of the individual antennas is related to the spacing of thearray. The size parameter X can be varied in order to achieve differentresonance wavelengths. In the arrays we studied in this work, X was 80nm. 99
9.3 Cross-section of the three types of samples examined in this study. a)the bare antenna sample, b) the reference sample with a dielectric spacerabove the antennas, and c) the superlens sample with layered metal anddielectric films above the antenna arrays. . . . . . . . . . . . . . . . . . 101
9.4 SEM image of a nanoantenna array (X = 80nm). The pattern is well re-produced with a gap size around 20nm. Some minor variations in antennashape can be observed, which can be ascribed to the finite metal grainsize. The slight rounding of the corners of the nanoantennas is accountedfor in our numerical simulations. . . . . . . . . . . . . . . . . . . . . . 101
9.5 Three types of NSOM scanning modes. The thick arrow represents illumi-nation of the sample. The thin arrows represent the collected or measuredlight. In this work we focused on collection mode NSOM (right panel) forour near-field measurements. . . . . . . . . . . . . . . . . . . . . . . . . 104
xv
Figure Page
9.6 NSOM scan (left) and intensity cross-section (right) of a bare antennaarray illuminated with perpendicular-polarized light at 620 nm. The an-tenna pairs can be observed as dark regions because they block some ofthe light transmitted through the substrate. . . . . . . . . . . . . . . . 106
9.7 NSOM scan (left) and cross-section (right) of a bare nanoantenna arrayilluminated with parallel-polarized light at 620 nm. In the cross-sectionscan, the antenna array boundary is at 4 μm. A periodic resonance isobserved that extends well beyond the boundaries of the array and decayswith distance from the array. In this resonant mode, the peak intensitiesare significantly higher than that of the incident light. . . . . . . . . . . 107
9.8 NSOM scans of the intensity distribution (left) and intensity cross-section(right) measured on a superlens sample for three different wavelengths.At 620nm (top) only the propagating mode is seen, at 650nm (middle) aweaker second mode starts to appear, and at 680 nm (bottom) the weakermode has grown in strength to equal the propagating mode. . . . . . . 108
9.9 Comparison of the NSOM intensity distributions for the same antenna ar-ray under three different conditions. In addition to the propagating mode,a second resonance mode was observed for the parallel polarization on asuperlens sample (top panel), which caused the appearance of frequencydoubling. No such mode was observed for the perpendicular polarizationon the same sample (middle), or for the parallel polarization on a refer-ence sample (bottom). All data was taken at an incident wavelength of680 nm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
9.10 Elliptically-shaped nanoantenna pair used as the unit cell of the array inthe FDTD simulations. The shape of these antennas corresponds moreclosely with the actual shape of the nanoantennas, as indicated in ourSEM results. In this image, white is metal (silver) and black is dielectricmaterial (glass). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
9.11 Representative FDTD near-field intensity maps. These maps were calcu-lated for the bare antenna sample with 620nm illuminating light at the par-allel polarization (left column) and the perpendicular polarization (rightcolumn). The maps show the intensity patterns 10 nm above the sample,averaged in a 150nm radius circle, and plotted for each field component.The corresponding intensity scales (arbitrary units) are also shown. Thex- and z-components dominate in the parallel polarization, but the y-component dominates in the perpendicular polarization. . . . . . . . . 117
9.12 NSOM scans and corresponding total near-field intensity simulations forthe bare antenna sample in both polarizations and at an incident wave-length of 620 nm. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
xvi
Figure Page
9.13 NSOM scans (upper panels) and corresponding total near-field intensitysimulations (lower panels) for the superlens sample in both polarizationsand at an incident wavelength of 680 nm. . . . . . . . . . . . . . . . . . 119
9.14 NSOM scans with unpolarized light at the edge of an antenna array. Theimage on the left shows the topography (height profile) of the sample.The antennas cover roughly 40% of the image. The image on the rightshows the corresponding NSOM intensity profile of the same region. Theintensity pattern continues beyond the array, indicating a propagating,diffraction-based mode. . . . . . . . . . . . . . . . . . . . . . . . . . . . 119
9.15 NSOM scans (upper panels) and corresponding total near-field intensitysimulations (lower panels) for the reference sample in both polarizationsand at an incident wavelength of 660 nm. . . . . . . . . . . . . . . . . . 120
A.1 Metal / dielectric interface used for surface plasmon polariton excitation. 135
A.2 Surface Plasmon Polaritons (SPPs). Distribution of free charge carriersoscillating at the metal / dielectric boundary. The distribution of the SPPmode can be seen by the red curve. . . . . . . . . . . . . . . . . . . . . 137
A.3 A coupled SPP mode will exist when the thickness of the metallic layer isbelow the decay length of the surface mode in an IMI structure. . . . . 138
A.4 A coupled SPP mode in a MIM structure. While the mode is confinedwell, most of the field is in the metal, and will therefore suffer from themetallic losses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
A.5 Geometry of the localized surface plasmon resonance. . . . . . . . . . . 141
B.1 Some of the external components of the GLAD system . . . . . . . . . 144
B.2 Some of the internal components of the GLAD system . . . . . . . . . 145
B.3 Screenshot of the GUI for the GLAD system. . . . . . . . . . . . . . . 148
xvii
SYMBOLS
m mass
c velocity of light
c0 velocity of light in free space
ε complex permittivity of a material
ε’ real part of the complex electric permittivity of a material
ε” imaginary (lossy) part of the complex electric permittivity of ma-
terial
μ material’s magnetic permeability
xviii
ABBREVIATIONS
AFM Atomic Force Microscope
AZO Aluminum doped Zinc Oxide
CMOS Complimentary Metal Oxide Semiconductor
DSP Double-Side Polished (silicon wafer)
EBL Electron Beam Lithography
EM Electromagnetic
FDTD Finite Difference Time Domain
FEM Finite Element Method
FESEM Field Emission Scanning Electron Microscope
FIB Focused Ion Beam
GLAD Glancing Angle Deposition
GRIN Graded Index
GZO Gallium doped Zinc Oxide
HMM Hyperbolic Metamaterial
HSQ Hydrogen Silsesquioxane
IR Infrared
ITO Indium Tin Oxide
LRSPP Long Range Surface Plasmon Polariton
LSPR Localized Surface Plasmon Resonance
MDC Metal Dielectric Composite
NIR Near Infrared
NSOM Near-Field Scanning Optical Microscopy
PDOS Photonic Density of States
QCM Quartz Crystal Monitor
xix
RIE Reactive Ion Etching
RPM Revolutions Per Minute
SEM Scanning Electron Microscope (refers to FESEM)
SERS Surface Enhanced Raman Spectroscopy
SPP Surface Plasmon Polariton
TO Transformation Optics
UV Ultraviolet
xx
ABSTRACT
West, Paul R. Ph.D., Purdue University, May 2015. Novel Techniques for QuasiThree-Dimensional Nanofabrication of Transformation Optics Devices. Major Pro-fessor: Alexandra E. Boltasseva.
Current nanofabrication is almost exclusively limited to top-down, two-dimensional
techniques. As technology moves more deeply into the nano-scale regime, fabrication
of new devices with quasi three-dimensional geometries shows great potential. One
excellent example of an emerging field that requires this type of non-conformal 3D
fabrication technique is the field of “Transformation Optics. This field involves trans-
forming and manipulating the optical space through which light propagates. Arbitrar-
ily manipulating the optical space requires advanced fabrication techniques, which are
not possible with current two-dimensional fabrication technologies. One step toward
quasi three-dimensional nanofabrication involves employing angled deposition allow-
ing new growth mechanisms, and enabling a new realm of quasi three-dimensional
fabrication.
Transformation optics also has potential for having a huge impact on one of the
most fundamental and impactful aspects of optics - the capability of fully control-
ling and manipulating the phase of light. For this purpose, dielectric metamaterial
arrays can be fabricated, altering the phase of light transmitted through the struc-
tures, while maintaining a high transmittance (low reflection). By fabricating these
structures with a high-index material (such as silicon), a large gradient in phase can
be implemented by adjusting the material’s effective filling fraction. Using these di-
electric metamaterial arrays, anomalous refraction and focusing is demonstrated in
films with thicknesses less than one wavelength.
1
1. PLASMONIC MATERIALS - CHALLENGES AND
APPROACHES
The field of Transformation Optics allows for a strong manipulation of an optical
wave as it passes through an artificially created material. In order to have this strong
control over an incident field, many devices require metallic components (with neg-
ative permittivity) to have complete control over the material’s permittivity. The
study of a wave’s behavior with these metals, (known as plasmonics), is a research
area merging the fields of optics and nanoelectronics by confining light with relatively
large free-space wavelength to the nanometer scale - thereby enabling a family of novel
devices. Current plasmonic devices at telecommunication and optical frequencies face
significant challenges due to losses encountered in the constituent plasmonic materi-
als. These large losses seriously limit the practicality of these metals for many novel
applications. Research in materials plays an important role in transforming ideas
into next-generation electrical and plasmonic technologies. Currently, plasmonic and
metamaterial devices have a lack of feasible materials (especially metals), required
to realize useful devices While current plasmonic technologies primarily rely on sil-
ver and gold, there are many other materials that exhibit metallic properties and
provide advantages in device performance, design flexibility, fabrication, integration,
and tunability. This paper provides an overview of alternative plasmonic materials
along with motivation for each material choice and important aspects of fabrication.
A comparative study of various materials including metals, metal alloys and heavily
doped semiconductors is presented. The performance of each material is evaluated
based on quality factors defined for each class of plasmonic devices. Most importantly,
this paper outlines an approach for realizing optimal plasmonic material properties for
specific frequencies and applications, thereby providing a reference for those searching
for better plasmonic materials.
2
1.1 Introduction
The speed of information processing has seen rapid growth in the past few decades
from the progress in scaling down the sizes of devices in micro- and nanoelectronics.
However, researchers are experiencing major difficulties in reaching speeds over a few
tens of GHz using this scaling approach due to fundamental limitations from RC-
delays and power dissipation in the devices. In contrast, photonics offers bandwidth
in the THz range [1]. However, conventional photonic elements, such as optical fibers,
require physical dimensions on the order of the wavelength of light (about a micron)
due to diffraction limitations. The difference in physical size between nanometer-scale
electronics and micrometer-scale photonic elements yields an incompatibility between
the two types of devices. Plasmonics merges the high bandwidth offered by photonics
and the nano-scale integration offered by nanoelectronics by coupling a photons en-
ergy with a free-electron gas, creating a subwavelength, oscillating mode known as a
plasmon [2–5]. Because plasmonic devices are capable of subwavelength confinement,
plasmonics forms the basis of the research area of nanophotonics. Plasmonics and the
recent birth of metamaterials [6–8] (for recent review on optical metamaterials see [9])
and Transformation Optics (TO) [10–12] are currently driving the development of
a family of novel devices with unprecedented functionalities such as subwavelength
waveguides [4, 13, 14], optical nanoantennas [15–24], superlenses [7, 25–28], optical
invisibility cloaks [11, 29–32], hyperlenses [33–36], planar magnifying hyperlens and
light concentrators [8, 37, 38].
Because the plasmon phenomenon in optical and telecommunication frequencies
typically originates from the collective oscillations of free charges in a material due
to an applied electromagnetic field, plasmonic devices generally require metallic com-
ponents, which have an abundance of free electrons. These free electrons provide the
negative real permittivity that is an essential property of any plasmonic material.
However, metals are plagued by large losses, especially in the visible and ultra-violet
(UV) spectral ranges, arising in part from interband electronic transitions. Even
3
the metals with the highest conductivities suffer from large losses at optical frequen-
cies [39, 40]. These losses are detrimental to the performance of plasmonic devices,
seriously limiting the feasibility of many plasmonic applications. In an attempt to
mitigate material losses, optical gain materials can be combined with metallic struc-
tures [41–55]. However, even the best gain materials available are barely enough to
compensate the losses in the metal. Because these losses are inherent to the con-
stituent materials, alternative plasmonic materials with lower losses are required to
develop robust plasmonic devices. Lower losses in such improved plasmonic compo-
nents can be readily compensated with existing gain materials.
Plasmonics could have a large impact on applications at telecommunication and
optical frequencies, and hence we begin this review with a survey of several potential
plasmonic materials (also see [56]). We compare the relative merits of these poten-
tial materials within the context of novel plasmonic devices to gain insight into the
suitability of each material in particular applications. In Sect. 1.2, we provide a brief
background on the various electromagnetic losses associated with solids at frequencies
in and near the visible range. In Sect. 1.3, we review the optical properties of various
plasmonic materials and also discuss the methodologies adopted in choosing potential
low-loss materials for plasmonics. Specifically, Sects. 1.3.1, 1.3.2, and 1.3.3 review
metals, metal-alloys, heavily doped wide-band semiconductors, and graphene respec-
tively. We formulate the figures-of- merit (or quality factors) for various classes of
plasmonic devices to effectively compare the performances of plasmonic materials in
Sect. 1.4. Finally, in Sect. 1.5, we present a comparative study of the performance of
the various potential materials based on figures-of-merit and other practical criteria.
We conclude the paper with a discussion that quantitatively identifies the best of the
reviewed material choices for each class of devices for various regions of the visible
and near-infrared (NIR) ranges.
4
1.2 Background
Polarization describes a materials interaction with electromagnetic waves. While
polarization can be electrical and/or magnetic in nature, the magnetic polarization of
naturally occurring materials is negligible for frequencies higher than several hundred
THz. The electrical polarization can be described by the materials complex electrical
permittivity or dielectric function, denoted by ε(ω). While the real part of the dielec-
tric function (denoted by ε1 or ε’) describes the strength of the polarization induced
by an external electric field, the imaginary part (denoted by ε2 or ε′′) describes the
losses encountered in polarizing the material. Thus, a low loss material is associated
with small values of ε′′.
Primary loss mechanisms in the NIR, visible, and soft UV frequencies may be
broadly classified as arising from phenomena related to conduction electrons and
bound electrons (interband effects) [57]. Losses for conduction electrons arise from
electron-electron and electron-phonon interactions, and from scattering due to lat-
tice defects or grain boundaries. Because the conduction electrons have a nearly
continuum of available states, their interaction with an electromagnetic field is well
approximated by classical theory. The Drude theory [58] describes this phenomenon
by treating conduction electrons as a three-dimensional free-electron gas. According
to the generalized Drude theory, the permittivity of a material can be written as
follows:
ε(ω)′ + iε(ω)′′ = ε(ω) = εint −ω2p
ω(ω + iΓ), (1.1)
ω2p =
ne2
ε0m∗ . (1.2)
In Eq. (1.1), γ = 1/τ where τ is the mean relaxation time of conduction electrons,
and εint is a contribution due to interband transitions; it is unity for the case of a
perfectly free-electron-gas. The plasma frequency (ωp) is given by Eq. (1.2), where
n is the conduction electron density, and the effective optical mass of conduction
5
Table 1.1Drude model parameters for metals. ωint is the frequency of onsetfor interband transitions. Drude parameters tabulated are not validbeyond this frequency.
Material εint ωp(eV ) Γ (eV) ωint (eV)
Silver [39, 59, 60] 3.7 9.2 0.02 3.9
Gold [39, 60] 6.9 8.9 0.07 2.3
Copper [39, 59, 60] 6.7 8.7 0.07 2.1
Aluminum [61,62] 0.7 12.7 0.13 1.41
electrons is m∗. In general, εint depends on wavelength (which is typically accounted
by including the Lorentz oscillators terms [57]), but for some spectral ranges it can
be roughly approximated as constant (see Table 1.1). Also, Γ can depend on the size
of the plasmonic particle. According to the classical theory, the total damping rate,
Γ, is the sum of damping rates due to electron-electron scattering, electron-phonon
scattering and lattice defects or grain-boundary scattering. The boundary scattering
rate depends on the size of the plasmonic particle, so that the relaxation rate for a
spherical particle of size R can be approximated as:
Γ = Γ∞ + AvFR
, (1.3)
where Γ∞ is the relaxation constant of the bulk material, vF is the Fermi velocity;
A depends on details of the scattering process, and is typically on the order of unity
[57, 63,64]. For simplicity, below we assume that Γ = Γ∞.
Because plasmonic applications require materials with negative ε0, Eq.(1.1) clearly
indicates that this requirement is satisfied for materials with a plasma frequency
higher than the desired frequency of application. Because metals tend to have large
plasma frequencies and high electrical conductivity, they have traditionally been the
materials of choice for plasmonics. In Table 1, we summarize the material parame-
6
ters for high-conductivity metals as reported in the literature. Among the metallic
elements, silver has the smallest Γ and is the best-performing choice at optical frequen-
cies. Gold, which has a larger Γ than silver, is often the metal of choice at lower NIR
frequencies, having the advantage of being chemically stable in many environments.
However, gold has high interband losses in the visible spectrum for wavelengths below
or about 500nm. Similarly, copper is plagued by large interband losses over most of
the visible spectrum. Thus, silver and gold have predominately been the materials
of choice for plasmonic applications around the optical frequencies. However, future
plasmonic applications demand even lower losses to fully exploit their potential.
Interband transitions, which form a significant loss mechanism in materials at
optical frequencies, occur when electrons jump to higher, empty energy levels caused
by absorption of incident photons. In metals, when a bound electron absorbs an
incident photon, the electron can shift from a lower energy level to the Fermi surface
or from near the Fermi surface to the next higher empty energy level. Both of these
processes result in high loss at optical frequencies.
In semiconductors and insulators, valence electrons absorbing the energy from a
photon shift into the conduction band, resulting in loss. This loss manifests as an
increase in ε′′, and can be treated using the formalism of the Lorentz oscillator model.
The two-level description of the absorption process results in a simple Lorentz model
given by Eq. (1.4) [65]:
εlk(ω) =flkω
2p,lk
ω2lk − ω2 − iωΓlk
. (1.4)
Here, flk corresponds to the strength of the oscillator at energy levels l and k,
ωlk is the resonant frequency corresponding to the difference between the energies
of levels l and k, Γlk is the damping in the oscillator accounting for non-zero line-
width of the peak, and ωp,lk is similar to the plasma frequency given by Eq. (1.2)
with the difference that n here refers to the concentration of electrons in the lower
occupied state. When there are many of such interacting energy levels, the effective
permittivity can be expressed as a summation over all allowed Lorentzian terms. This
7
is a popular approach utilized in the Drude-Lorentz model to reasonably approximate
the dielectric function of metals [66]. In general, solids with a periodic lattice have
electronic energy levels which exist as bands instead of discrete levels, requiring a
Joint-Density-of-States description and integration over all the allowed transitions
at any given photon energy (a more detailed discussion of this formulation is found
in [65]).
To illustrate the impact of interband transitions on losses in a material, Fig. 1.1
shows the imaginary part of permittivity for copper. The free-electron and inter-
band transition contributions to loss are shown along with the values extracted from
experimental results [39]. The peak in the experimental ε′′ curve at 2.1 eV clearly
corresponds to interband transitions; this peak is the result of electronic transitions
from the filled L3 band to the Fermi surface [59]. Similarly, the peak at 5.2 eV is due
to X5 → X40 transitions and L2 → L1 transitions [59]. Table 1 shows the frequency
ωint that marks the onset of significant loss due to interband transitions in several
selected metals.
The direct transitions discussed above form an important loss mechanism in both
semiconductors and insulators. In direct bandgap semiconductors, the bandgap cor-
responds to the onset of interband transitions. In indirect bandgap semiconductors,
indirect transitions contribute to loss for photon energies exceeding the bandgap be-
fore the direct transitions set in. For photon energies below the bandgap, there can
be appreciable losses due to various mechanisms such as trap-assisted transitions (e.g.
nitrogen levels in GaP:N [67]), generation of excitons (especially for wide bandgap
semiconductors and insulators [68–70]) and transitions between impurity levels [71].
1.3 Survey of Alternative Plasmonic Materials
This section focuses on potential candidates for low-loss plasmonic materials in
the NIR, visible, and near-UV spectral ranges. Various metals, metal-alloys, metallic
com- pounds and semiconductors that can offer advantages as plasmonic materials are
8
Fig. 1.1. The losses in Cu shown as the sum of interband lossesand free electron losses [39, 59]. Annotations identify the interbandtransitions responsible for peaks in ε′′
identified and discussed in terms of their relevant properties. Discussion is categorized
into subsections based on the class or type of material reviewed. Metals are considered
first, followed by metal-alloys in the second subsection. The third subsection focuses
on doped semiconductors, while the last discusses graphene.
1.3.1 Metals as Candidates for Plasmonics
As discussed in Sect. 1.2, metals are candidates for plasmonic applications be-
cause of their high conductivity. Among metals, silver and gold are the two most
often used for plasmonic applications due to their relatively low loss in the visible
and NIR ranges. In fact, almost all of the significant experimental work on plasmon-
ics has used either silver or gold as the plasmonic material. Silver has been used for
the demonstration of a superlens [26,27], a hyperlens [35], a negative-refractive-index
9
material in the visible range [72], and extraordinary optical transmission [73]. Gold
was used for the first demonstration of a negative-refractive-index material in the
NIR [74], many studies on Surface-Enhanced Raman Scattering (SERS), the fabri-
cation of plasmon waveguides, and numerous Localized Surface Plasmon Resonance
(LSPR) sensors (see for instance, [75]). While metals other than silver and gold have
been used in plasmonics, their use is quite limited, as their losses are higher than
those of silver and gold. For instance, platinum and palladium have been used as
plasmonic materials in systems where the catalytic activity of the plasmonic material
is important to the overall device functionality [76,77]. In addition, nickel films have
been reported to have surface plasmon-coupled chemiluminescence, which may merit
the use of nickel in particular plasmonic applications.
Among the alkali metals, sodium and potassium have the lowest losses [78, 79].
In fact, these losses are comparable or even better than that of silver. Although
there have been several theoretical studies on alkali metals [79], they will not be
discussed in this section, as their potential has not been experimentally verified to
our knowledge. In pure elemental form, these alkali metals are very reactive to air
and water, and therefore they must be stored in mineral oil or Ultra High Vacuum
(UHV) environments to avoid highly energetic and dangerous reactions. Such extreme
restrictions have made fabrication with alkali metals prohibitive. While depositing
alkali metals can be a straightforward process, accomplished with an alkali metal
dispenser, other fabrication and characterization obstacles must be overcome before
alkali metals find use in plasmonics. In the following section, we will discuss low-loss
noble metals (silver, gold and copper) and aluminum. The plots of ε’ and ε′′ of these
four metals along with potassium and sodium are shown in Fig. 1.2
As previously mentioned, silver has the lowest loss in the visible and NIR ranges.
However, in terms of fabrication, silver degrades relatively quickly and the thickness
threshold for uniform continuous films is around 1223nm [80–82], making silver less
suitable for TO devices (discussed in Sect. 5). Additionally, silver losses are strongly
dependent on the surface roughness [57]. Gold is the next-best material in terms of
10
Fig. 1.2. Real (a) and imaginary (b) parts of the permittivities of Ag,Au, Na, K, and Al. The data for Ag, and Au are taken from [39], andthose of Al, Na, and K are from [78]
loss in the visible and NIR ranges. Compared with silver, gold is chemically stable
and can form a continuous film even at thicknesses around 1.57nm [83,84]. It is very
important to note that films deposited with thicknesses below the percolation thresh-
old are semi/discontinuous with drastically different optical properties compared to
uniform films [85,86]. These fabrication complications make these materials undesir-
able at thicknesses below the percolation threshold when continuous films are needed.
Silver and gold films can be fabricated by various physical vapor deposition (PVD)
techniques and nanoparticles and metal-coated nanoparticles can be synthesized by
liquid chemical methods. Typical PVD methods include electron-beam/thermal evap-
oration and sputtering. In liquid chemical methods, chloroauric acid (H[AuCl4]) and
silver oxide (Ag2O)/silver nitrite (AgNO4) are commonly used for gold and silver,
respectively.
Because copper has the second-best conductivity among metals (next to silver),
it is expected to exhibit promising plasmonic properties. Indeed, ε′′ of copper is
comparable to that of gold from 600-750nm. Considering the cost of silver and gold,
copper would be a good candidate to replace silver and gold as a plasmonic material
11
if the performance of copper were tolerable. Unfortunately, fabricating devices with
copper is challenging, as it easily oxidizes and forms Cu2O and CuO. A systematic
study of the oxidation effects on copper for LSPR modes is found in [87]. In their
results, Chan et al. have demonstrated that oxide-free nanospheres exhibit a sharp
and narrow LSPR peak comparable to that of silver and gold.
Aluminum has not been an attractive plasmonic material due to the existence of
an interband transition around 800nm (1.5 eV), resulting in large ε′′ values in the
visible wavelength range (see Fig. 1.2). However, in the UV range, ε’ is negative even
at wavelengths smaller than 200nm where ε′′ is still relatively low. Thus aluminum
is a better plasmonic material than either gold or silver in the blue and UV range.
It is important to note that the ε’ values of silver and gold do not become positive
until wavelengths greater than 326nm and 207nm, respectively. Aluminum is easily
oxidized and very rapidly forms an aluminum oxide (Al2O3 ) layer under atmospheric
conditions, making device fabrication with aluminum challenging. The thickness of
this Al2O3 layer is typically 2.5-3nm [88], and the presence of this oxide layer results
in a red shift in LSPR peak position [89]. Despite these challenges, aluminum has
been used in plasmonic systems in the UV-blue spectral region such as to study
LSPR [88, 89], surface plasmon polariton (SPP) propagation [90], surface-enhanced
fluorescence [91, 92], and Raman spectroscopy [93, 94].
1.3.2 Metallic Alloys
Metallic alloys, intermetallics and metallic compounds are potential candidates
for alternative plasmonic materials owing to their large free electron densities. This
section primarily discusses the various techniques employed to tune the optical charac-
teristics of metals by making alloys. Metallic compounds such as magnesium diboride
(MgB2) are not discussed here due to their poor performance as plasmonic materials
around optical frequencies [95–99]. Similarly, intermetallics such as silicides, which
12
are reported to be plasmonic materials, will not be discussed owing to their large
losses in the NIR and visible spectrum [100–105].
Noble-Transition Alloys
Because of the strong plasmonic performance of noble metals, one approach to
improve these materials is by shifting their interband transitions to another (unim-
portant) part of the spectrum. This can be achieved by alloying two or more elements
to create unique band structures that can be fine- tuned by adjusting the proportion
of each alloyed material.
Noble-transition metal alloys are one interesting set of potential alternative plas-
monic candidates. Bivalent transition metals, such as Cadmium and Zinc, when
doped into monovalent noble metals contribute one extra electron to the free-electron
plasma [106]. This results in n-type doping of noble metals, which raises the Fermi
level, increases ωp, and shift the threshold for interband transitions, thereby modify-
ing the optical spectra of the alloy. By changing the Fermi level of a metallic layer,
one can, in principle, reduce the absorption at a specific wavelength. This could
be accomplished, for example, by shifting the Lorentzian peak to some other wave-
length that is unimportant for a particular application. This process of manipulating
and fine-tuning a materials electronic band structure to achieve desirable electronic
properties is referred to as band engineering.
The particular experiment detailed in [106] involved n-doping gold with cadmium
and employed samples with pre-determined stoichiometries that were purchased from
commercial vendors. Alloying gold and cadmium creates a unique band structure,
shifting the peak losses to new frequencies and resulting in higher losses in one fre-
quency range, with simultaneously lower losses in another range. To illustrate this
point, Fig. 1.3 shows a simulation demonstrating how doping gold with cadmium
shifts the interband transition peaks, confining high losses to one region while lower-
ing losses almost everywhere else in the spectrum. This method of raising the Fermi
13
level by small amounts can continue for low doping levels (<10% volume), but the
technique will break down as the doping levels become high enough to significantly
modify the materials band structure. This technique may be extended to different ma-
terial combinations, creating unique band structures optimized for specific frequencies
and applications.
Fig. 1.3. By courtesy of Dr. M. Noginov and Dr. V. Gavrilenko,Norfolk University [106]) Numerical simulation detailing the shift ininterband transition peak and modified band structure when Au [39]is doped with 3.3 at.% Cd. The dashed curve shows the imaginarypermittivity for the undoped gold, while the solid curve is the resultfor the doped alloy. The doping process combines the losses frompeaks I & II into a single, confined high-loss region, while leavinglower losses elsewhere.
Alkali-Noble Inter-Metallic Compounds
Alkali-noble metal inter-metallic compounds are another group of candidates for
low-loss metals because the Group I alkali metals exhibit the strongest free-electron-
like behavior [107]. As far back as 1978 [108], the permittivity of Li2AgIn was exper-
14
imentally measured, exhibiting zero-loss permittivity values at 2 eV without mention
of the implication of this result for plasmonic devices. Note that this paper presents
data showing negative losses, which raises some doubts about the accuracy of mea-
surements or parameter extraction. While many alkali-noble metal binary compounds
have been presented as alternative plasmonic materials [107], the compound predicted
to show the most promise is potassium gold (KAu), which has been calculated to have
zero interband losses below its unscreened plasma frequency at 1.54 eV. However, be-
cause of Drude losses, the crossover point is 0.5 eV. Because KAu does not have
negative ε values in the telecommunication and visible frequency ranges, it cannot be
considered a plasmonic candidate for applications in these spectral ranges.
Fabrication of alkali-noble compounds can be challenging. Just bringing two met-
als of significantly different properties together to form an alloy can be a non-trivial
task. The vapor pressures of potassium and gold differ by 10 orders of magnitude and
their surface energies differ by an order of magnitude, making the alloying process
difficult. Assuming these compounds behave similarly to pure alkali metals, these
highly reactive alloys must either be characterized in-situ or be passivated prior to
removing them from the fabrication chamber in order to prevent rapid oxidation.
Passivation would allow for further optical characterization of the fabricated sample
using ellipsometry, prism coupling, SPP propagation, and other techniques, but the
passivation itself may alter the surface properties of the sample as well as limit appli-
cability of such films for real device fabrication. Because such compounds have not
been extensively studied in the past, the phase, stoichiometry and growth kinetics of
these alloy systems are not well understood.
1.3.3 Semiconductors
Semiconductors are conventionally regarded as dielectric materials for frequencies
above several hundred THz. However, semiconductors can actually exhibit a negative
real permittivity in this spectral region under certain circumstances [109–112]. Due
15
to the ease of fabrication and flexibility in tuning their properties such as carrier
concentration, semiconductors are also potential materials for plasmonics. In order
to qualify as a low-loss plasmonic material, the bandgap and plasma frequency of the
semiconductor both must be larger than the frequency range of interest. While a
large plasma frequency ensures a negative real permittivity, a large bandgap ensures
almost no interband transition losses. Semiconductors can exhibit negative ε’ in IR
frequencies when heavily doped [109–111] or in resonance (e.g. phonon resonance in
silicon carbide [78, 112, 113]). Because resonance is a narrow-band phenomenon and
phonon resonance occurs at low frequencies, here we con- sider only heavily doped
semiconductors as possible low- loss plasmonic materials. Thus, a wide bandgap,
heavily doped semiconductor with high carrier mobility can qualify as a low loss
plasmonic material around the optical frequencies.
Despite the abundance of semiconductors with large bandgap values (> 1.5 eV)
and high carrier mobilities, very high doping levels are necessary to bring the crossover
frequency of semiconductors into the optical range, and achieving these doping levels
is challenging. Hoffman et al. [111] reported that doping gallium arsenide to 7× 1018
cm−3 can raise the crossover frequency (where ε’ changes from negative to positive) to
about 9μm. However, to bring the crossover frequency near the optical range, a doping
level of at least 3× 1020cm−3 is required. The necessity of doping semiconductors so
heavily raises concerns about the solid solubility limit, the fraction of dopants that
would be active, and doping compensation effects [114, 115]. Another major concern
at such high doping levels is retaining the high carrier mobility that is essential for
low losses. Due to these issues, plasmonics in the optical spectrum has remained
mostly out-of-reach for semiconductor materials.
However, indium-tin-oxide (ITO) has been shown to be a potential plasmonic
material in the NIR region [116–120]. ITO is a transparent, conducting oxide typically
consisting of 90% wt indium oxide (In2O3 ) and 10%wt tin oxide (SnO2). ITO has
been widely studied in the field of optoelectronics. Because ITO is non-stoichiometric,
predictions show its plasma frequency can be engineered between 0.44 eV and 6.99 eV
16
by varying the tin (Sn) doping level in In2O3 up to 45%wt. Experimentally, the plasma
frequency has been measured between 0.78 and 2.13 eV [110,121,122]. Robusto et al
have demonstrated SPPs in ITO between 1.8μm and 1.9μm [116], which was followed
by many other groups [117–120] reporting SPPs in the NIR region. Therefore, ITO
appears to be an appealing plasmonic material in the NIR and optical frequency
ranges.
Because ITO is a non-stoichiometric compound, its optical properties largely de-
pend on the growth/deposition processes and annealing conditions, including the
temperature and ambient gasses [110]. Sputtering and laser ablation techniques have
reliably produced quality films of ITO [123]. Post-deposition annealing in nitrogen
has been shown to produce more conductive and less transparent films due to in-
creased oxygen vacancy (VO) defects [124]. On the other hand, less conductive and
more transparent films are produced by annealing ITO in an oxygen ambient [124].
In our own experiments, we have observed significant changes in the dielectric func-
tion of e-beam evaporated ITO films annealed in different ambient environments, as
shown in Fig. 1.4. While ITO films annealed in oxygen do not show negative ε’ in
the spectrum of interest, the films annealed in nitrogen ambient do show negative
real permittivity. Fig. 1.4 also shows that ITOs properties depend on the annealing
temperature. A higher annealing temperature increases the conductivity of the ITO
film and reduces the loss within the wavelength range of interest. It is important to
note that the loss in ITO films is comparable to that of silver in the NIR range but
is significantly lower than the losses in silver at longer wavelengths.
Other than ITO, high performance conductive zinc oxides such as Aluminum Zinc
Oxide (AZO) and Gallium Zinc Oxide (GZO) can be promising low-loss alternatives in
NIR. These conductive zinc oxides are widely studied for applications in transparent
electronics. Based on the optical characteristics of these films reported in literature,
we have found that AZO and GZO can have significantly lower loss than silver at
telecommunication wavelengths which are of particular importance for photonics and
nanophotonics applications (see Fig. 1.5) [125–127]. While AZO can exhibit losses
17
Fig. 1.4. Real (a) and imaginary (b) parts of permittivity of ITOannealed at various conditions (N2, 450
◦C; N2, 650◦C; O2, 450◦C; O2,
650◦C).
Fig. 1.5. Real (a) and imaginary (b) parts of permittivity of AZOand GZO obtained from parameters reported in reference [125]. Thelosses in AZO and GZO are much smaller than that of silver [39] atthe telecommunication wavelength.
more than three times lower than that of silver at the wavelength of 1.5μm, GZO
being only slightly inferior to AZO, can exhibit lower losses too.
18
Similar to other conductive oxides, AZO and GZO are non-stoichiometric, and
deposition conditions play a crucial role in achieving the desired properties. High
quality thin films of AZO and GZO may be produced by sputtering or laser abla-
tion. Deposition temperature, oxygen partial pressure during deposition and dopant
concentration must be optimized in order to achieve low loss as well as negative real
permittivity [109,125–129]. For example, M. H. Yoon et al. report that large doping
of zinc oxide does not necessarily increase the carrier concentration [130]. In AZO,
a large doping level results in the formation of ZnAl2O4 , which does not increase
carrier concentration, but adversely affects the carrier mobility through increased
scattering. This causes the zero-cross-over of real permittivity to shift towards longer
wavelengths. We observe this happening in Pulsed Laser Deposited (PLD) AZO films
with 2%wt Al2O3. Evidently, lower Al2O3 concentration of about 0.8 %wt produces
AZO films with ε’ -cross-over at a wavelength smaller than 1.5μm [125]. With losses
being much smaller than in silver at this wavelength, AZO is a promising low-loss
alternative material for plasmonics in NIR.
Aside from oxide semiconductors, III-V semiconductors (e.g. GaAs, GaN, GaP)
and SiC are potential candidates for plasmonics in the NIR and optical spectral
ranges. However, heavy doping could again be a problem that must be addressed
when considering these materials as options for alternative plasmonic materials.
1.3.4 Graphene
Graphene is another material that has generated excitement in the research com-
munity due to its unique band structure and high carrier mobility [131–134]. Graphene
is a two-dimensional system - enabling excitation of surface plasmons (SP) similar to
the surface plasmons on metal/dielectric interfaces. However, these two-dimensional
plasmons in graphene exhibit a dispersion relation different compared to plasmons
in three dimensions [135–137]. Some schemes for plasmon based THz oscillators in
graphene have already been proposed in literature [138–140]. These plasmon modes
19
can possibly exist up to near-IR frequencies. However, in order to evaluate the po-
tential of graphene as an alternative low loss plasmonic material, the losses in the
plasmon modes must be evaluated [141].
It can be expected that interband transitions contribute significantly to losses be-
cause of the zero band-gap in graphene. These interband transitions occur above a
threshold determined by Fermi energy and plasmon wavevector [136]. However, this
threshold can be shifted to frequencies beyond the region of interest by larger doping,
which increases the Fermi energy. It has already been experimentally demonstrated
that the interband threshold can be tuned by varying electrical doping [142]. Be-
low the interband threshold, the losses are primarily due to impurity scattering and
excitation of optical phonons together with electron-hole pairs. Jablan et al. have
analyzed the electron relaxation times due to different loss mechanisms in graphene,
and demonstrate that graphene may inherently contain lower losses relative to con-
ventional metal/dielectric interfaces up to frequencies corresponding to 0.2 eV [141].
Initial theoretical estimates indicate that graphene is a good plasmonic material for
THz applications. However, at NIR frequencies, losses in graphene may still be com-
parable to noble metals. This makes graphene less attractive as an alternative plas-
monic material at the telecommunications and visible wavelengths.
1.4 Quality Factors
Quality factors, or figures-of-merit, form a common platform to compare the per-
formances of various materials used in different applications over a wide frequency
band. Although the loss in a material characterized by ε′′ is a necessary indicator
of performance, the real part of permittivity ε’ is also important in quantifying the
overall material quality in many devices. Because the field distribution in a material
depends on ε’ and the loss depends on ε′′, performance metrics or quality factors for
a plasmonic material are generally a function of both ε’ and ε′′. Considering that
different applications can have different definitions for the quality factors [143–146],
20
our discussion is focused on four major classes of plasmonic devices: LSPR based
devices, SPP waveguides, TO devices and superlens. It is important to note that
the following discussions are valid only in the range of frequencies for which ε’ is
negative. For metals and metal-like materials such as heavily doped semiconductors,
this translates to frequencies below the crossover frequency. It should also be noted
that in the following discussion, the term metal is used for both metals and metal-like
materials for brevity.
In the first part of this section, the quality factors of LSPR and SPP systems
are considered and are denoted as QLSPR and QSPP, respectively. LSPR and SPR
systems produce local field enhancement at the surface of metallic components. Hence
their quality factors can be defined as follows:
Qf =(Enhanced local field)
(Incident field)(1.5)
Quality factor for LSPR depends significantly on the shape of the metal nanopar-
ticles. For a sphere, QLSPR is given by Eq. (1.6):
QLSPR(ω) =−ε′(ω)ε′′(ω)
. (1.6)
For a cigar-shaped spheroid, Eq. (1.6) becomes Eq. (1.7):
Q′LSPR(ω) =
ε′(ω)2
ε′′(ω). (1.7)
For SPR, the quality factor QSPR assumes the same form as Eq. (1.6). QSPP
can be defined as the ratio of the real part of the propagation wavevector (k′x) to the
imaginary part (k′′x) [147]:
Q′SPP (ω) =
k′x(ω)k′′x(ω)
=ε′m(ω) + εd(ω)
ε′m(ω)εd(ω)ε′m(ω)
2
ε′′m(ω), (1.8)
where εm is the permittivity of the metal, and εd is the permittivity of the sur-
rounding dielectric material. If |ε′m| � εd, Eq. (1.8) can be simplified as follows:
21
Q′SPP (ω) =
ε′(ω)2
ε′′(ω). (1.9)
It may be noted that QSPP has the same form as Q′LSPR defined for spheroid
nanoparticles. The quality factors for LSPR and SPP are shown in Fig. 1.6. This
figure does not include semiconductors and alloys, as their quality factors are much
lower than the rest. Eqs. (1.6) & (1.9) explain how QLSPR and QSPP become large
when a material has a large, negative ε′ and a small ε′′. These equations clearly
convey why conventional plasmonic materials such as silver and gold, which have a
large, negative ε′ and a low ε′′, have been the plasmonic materials of choice for most
applications.
Fig. 1.6. Quality factors for localized surface plasmon resonances(QLSPR) is shown in panel (a), and surface plasmon polaritons qualityfactor (QSPP ) is shown in panel (b). The permittivity values used tocalculate the presented quality factors are the same as those shown inFig. 1.2
Transformation optics (TO) devices, however, require a different figure of merit
due to the nature of TO devices. These devices typically need materials with a real
part of effective permittivity close to zero at the operating frequency [12]. Thus,
TO devices require the response of metallic components to be nearly balanced by
22
that of dielectric components (which typically have εd ∼ 1). Hence, for practical
values of metal filling factors, the magnitude of ε′m of metal must be comparable in
magnitude (and opposite in sign) to that of the dielectric component. Thus, plasmonic
components of TO devices operate near their crossover frequency where ε′ is negative
and small in magnitude. Thus, in this case, only the losses (ε′′) are relevant in defining
the quality factor:
QTO =1
ε′′m(where − ε′m ∼ εd ∼ 1) (1.10)
We now turn our attention to the superlens and its resolution limits. The resolu-
tion limit of superlens can be defined through Eq. (1.11):
Δ
d=
−2π
ln(−ε′′
2ε′) (1.11)
where Δ is the minimum resolvable feature size and d is the thickness of the
superlens [148]. The value Δ/d can be considered as the normalized resolution of the
superlens. For the purpose of comparative studies using quality factors, we define
the inverse of Δ/d as the superlens quality factor QS. For the sake of comparison,
the host material is assumed to be air, hence ε′ of the superlens is set to -1 for the
following discussion. Therefore, QS can be expressed as:
QS =d
Δ=
− lnε′′
22π
(where ε′ = 1). (1.12)
Quality factors give a quantitative assessment of the performance of plasmonic
materials in their respective categories. However, practical considerations arising
from fabrication and integration issues must be considered before choosing the best
material.
23
1.5 Comparative Studies
A summary of the figures-of-merit for various materials discussed in the previous
sections is provided in Table 1.2. While quality factors describe how well a material
will perform for various applications, there are limiting issues in terms of processing
and fabrication. For example, alkali metals are difficult to work with because they are
extremely reactive in air ambient environments. Thus, alkali metals have not been
used in plasmonic applications regardless of their high quality factors. In addition,
silver and aluminum are not ideal materials for the fabrication of plasmonic devices
because these materials easily oxidize when exposed to air, which can significantly al-
ter their plasmonic properties. Other fabrication issues can arise in particular designs,
such as the formation of extremely thin metallic films and the controlled synthesis of
metallic nanoparticles.
24
Tab
le1.2
Tab
lecomparingvariou
splasm
onic
metalsresearched
inthisstudy
LSPR
&SPR
SPP
TO
Devic
es
Superle
ns
Com
ments
Materia
l
Maxim
um
QLSP
RM
axim
um
QSP
PQ
TO
QS
QLSP
R(λ
)(1
.5μm)
QSP
P(λ
)(1
.5μm)
(λ)
(λ)
Ag*
392
39.3
23413
4530
1.82
0.3
Good
forLSPR
&SPP
(1.08μm)
(1.08μm)
(326nm
)(3
39nm
)
Au*
16.66
10.63
1410
1140
0.29
-0.13
Good
forLSPR
(0.89μm)
(1.94μm)
(207nm
)(2
52nm
)
Al
13.56
5.55
2677
1315
26.32
0.52
Good
forLSPR
inUV
(0.113μm)
(2.5μm)
(82nm
)(1
14nm
)
Na*
37.8
27.3
1889
1179
NA***
0.48
Diffi
cult
topro
cess
(1.00μm)
(2.25μm)
(312nm
)
ITO
*
2.72
NA**
16
NA**
1.54
0.13
Good
forTO
inNIR
(2.3μm)
(2.3μm)
(1.69μm)
(1.88μm)
AZO
3.28
1.46
33.1
2.33
2.16
0.179
Good
forTO
inNIR
(2.26μm)
(2.5μm)
(1.3μm)
(1.46μm)
GZO
1.8
0.923
15.96
1.01
1.22
0.087
Good
forTO
inNIR
(2.3μm)
(2.5μm)
(1.32μm)
(1.48μm)
*Ag
and
Au
data
endsat2μm
,Na,K
data
endsat2.25μm
,and
ITO
data
endsat2.3μm.
**Cro
ssoverfrequency
forth
ese
mate
rials
occurs
ata
wavelength
above1.55μm
.Thus,
quality
facto
rsare
notapplicable
atth
ete
lecom
munication
wavelength
.
***
Cro
ssoverfrequency
data
isnotavailable.
25
Therefore, despite the fact that sodium and potassium have the highest QLSPR
and QSPP values next to silver, they are extremely difficult to work with, and are
therefore probably not practical from a fabrication standpoint. In most cases, silver is
by far the best material in terms of quality factor, but it is associated with problems
such as oxidation and cost. Aluminum has the advantage of having an extremely high
plasma frequency, and it is the only reviewed material that acts as a metal in the UV
part of the spectrum. However, aluminum also oxidizes quite easily, which can cause
issues in terms of fabrication.
Quality factors for TO devices and superlens indicate that alkali metals can be
a good choice. However, they have problems with processing and hence are not the
material of choice. Aluminum has a high QTO value, but is probably not particularly
good for TO applications. This is due to the fact that at the Al crossover wavelength
of 81nm, the thickness of the aluminum layer can be at most 8nm for effective medium
theory to hold. In this range, film roughness, as well as the formation of oxidation
layers, could be detrimental to the plasmonic properties of the aluminum structure.
However, Aluminum will perform well as a superlens, if these issues can be resolved.
Silver also suffers from similar fabrication problems. From the alkali-noble metal
alloys, KAu is a possible candidate for TO or superlens applications in terms of
the materials quality factor, but there are serious challenges with the synthesis and
chemical stability of KAu. In contrast, doped zinc oxide and indium-tin-oxide are
realistic choices for TO devices in the NIR range including the telecommunication
wavelength, which is particularly important for nanophotonics circuitry. With the
optimization of processing conditions, these materials can outperform silver for TO
applications, potentially enabling unsurpassed control of light on the nanoscale.
1.6 Conclusions
We have discussed the optical properties of different plasmonic materials, including
a comparison of their predicted performance metrics in terms of quality factors. The
26
comparative study shows that there is not a single clear choice for the best low-loss
plasmonic material for all applications. Our comparison demonstrates that silver
dominates all of the materials we considered in terms of its quality factors in LSPR
and SPP applications in the visible and NIR ranges. However, silver is not the
clear choice as a low-loss plasmonic material for other applications such as TO and
superlens. Even though alkali metals and aluminum have high quality factors for
TO devices and superlens, they pose processing challenges. Thus, silver is the best
material for a superlens in the near UV. In NIR, AZO may be the best material for
TO devices and superlensing, followed by ITO and GZO. Furthermore, these oxide
semiconductors can work well at the telecommunication wavelength, which makes
them very important substitutes for conventional materials such as gold and silver.
A materials quality factor describes how well a material performs, but it does not
give insight into other aspects such as ease of processing and feasibility of integration.
A final choice of materials requires a trade-off between quality factor, fabrication
practicality, and cost. As an example, the material cost of gold and silver prohibit
their wide-scale adoption in cost-driven markets such as photovoltaics.
With the rapid development of nanophotonics, it is clear that there will not be
a single plasmonic material that is suitable for all applications at all frequencies.
Rather, a variety of material combinations must be fine-tuned and optimized for
individual situations or applications. While several approaches and materials have
been presented, the problem of losses in plasmonic materials remains open-ended. An
improved plasmonic material has the potential to make an enormous impact on both
optics and nanoelectronics by allowing for a new generation of unparalleled device
applications. We expect the comparative study presented herein to be useful in the
elimination of poor choices, and it will serve as a guide in making the optimum choice
for a low-loss plasmonic material in various applications.
27
2. NANOWIRES GROWN WITH GLANCING ANGLE
DEPOSITION (GLAD)
Exploring and developing new and higher performance-based plasmonic materials is
the first step for practical and realizable Transformation-Optics devices. However,
many applications need non-conformal and films with gradient thicknesses that are
not possible with traditional, top-down, 2-Dimensional fabrication. As technology
moves forward towards Transformation Optics and other electronic technologies, in-
novation relies on new and 3D fabrication techniques.
2.1 Comparing Traditional PVD to GLAD
Physical Vapor Deposition (PVD) is an extremely common and developed tech-
nique used for depositing thin films on substrates. Using this technique, energy is
added to the source material - causing it to evaporate under vacuum. The evaporated
material will travel in a linear “line-of-sight” manner from the source to the substrate.
The sample is typically held directly above the source material at an angle normal to
the deposition. The films deposited in this manner onto the substrate will typically
be planar and uniform in thickness due to the relatively even deposition flux across
the substrate. When a mask is applied on the substrate, the line-of-sight nature of
the evaporation will deposit material relatively evenly both on the top of the mask,
and onto the substrate through the mask opening(s).
As opposed to typical deposition systems (where the sample’s angle and rotation
are fixed), Glancing Angle Deposition is a PVD process that allows full control over
the angle and rotation of the sample. With these added degrees of control, many
of the previous assumptions about the films deposited in PVD evaporation must be
reconsidered when the sample is rotated and/or the flux is deposited at an angle.
28
Using Glancing Angle Deposition (GLAD), this line-of-site behavior can be exploited
to produce a variety of films with non-planar geometries for new optical and electrical
devices. For example, when the substrate is rotated to a large, glancing angle (above
about 65◦), nanowires will grow (not continuous films). When materials are deposited
at an angle over a mask, non-planar films can be formed behind the mask. Similarly,
when materials are deposited on an angle over non-planar structures, non-uniform
structures can be created along curved surfaces. This fabrication approach shows
great promise in the Transformation Optics and metamaterials community to develop
materials with unprecedented control over the flow of light. A variety of interesting
and exciting devices can be fabricated using this fabrication technique that would be
difficult or impossible to do without it.
2.2 Background
Historically, most Glancing Angled Deposition (GLAD) fabrication has been fo-
cused on various types of nanowire fabrication. When a small amount of material
is first deposited on a substrate, rather than forming a thin and continuous film,
the material will begin by forming small islands. A good example of this process is
when silver is deposited on a silica substrate. For those unfamiliar with Ag thin film
deposition on Silica, the growth mechanisms involved are actually quite nontrivial,
and have been studied extensively in the past. Due to surface energy differences be-
tween Ag and Silica, rather than forming a smooth continuous film, Ag will transition
from small island formations to a percolated film, and eventually continuous films at
around 0-10nm, 10-20nm, and 20nm respectively. When Ag is deposited on a Silica
substrate at a glancing angle (larger than ∼65 ◦), a very different growth mechanism
occurs. At low deposition thicknesses, islands will form at random locations on the
substrate (similar to traditional evaporations). However, because the material flux is
incident at such high angles, the small islands will cast shadows behind them block-
ing the silver from depositing onto these areas. Because this shadowing effect allows
29
for the Ag to be deposited in some areas while not others, growth will only occur
in the non-shadowed areas effectively creating nanowires. This growth mechanism
is somewhat similar to the way in which trees grow in a forest. After the seeds are
randomly arranged on the forest floor, only the seeds that get sun will grow into trees.
As the trees become larger, they will capture more light, and continue growing, while
those left in the shadow will no longer grow. An illustration of this nanowire growth
mechanism is shown in Fig. 2.1.
Fig. 2.1. Growth mechanism for nanowire growth using GLAD. Thered arrows represent silver deposited at an oblique angle to the sub-strate. The red ellipses represent actively growing nanowires, whilethe gray ellipses represent the nanowires that have been shadowedand are no longer growing.
One detail of importance in Fig. 2.1 is that the nanowires grow parallel to one
another, but not antiparallel to the incident flux (as might be expected). This angle
of growth can be very roughly approximated using Eq. (2.1)
30
β = α− arcsin
(1− cos(α)
2
)(2.1)
where α is the angle of material deposition, and β is the angle of nanowire growth
[42] but a more exact calculation for the growth angle would involve many other vari-
ables, including what material is deposited, vacuum pressure, substrate temperature,
evaporation rate, etc.
Preliminary fabrication testing of nanowire growth was conducted by depositing
silver on a silicon dioxide substrate. Simultaneously, wires were also grown on a silicon
dioxide substrate with a very thin (15nm) ITO coating. Side- and top-views of this
fabricated sample are shown in Fig 2.2. The side view displays the deposition angle,
and the angle of wire growth. The top view shows nanowires with aspect ratios of
more than 11:1.
Fig. 2.2. Side and top views of the randomly grown array of Ag nanowires
2.3 Random Nanolasing
A laser/spaser can be created around randomly oriented structures that scatter
light randomly. In the case where these random structures scatter light in a “loop”,
an efficient feedback system can be formed. Gain medium surrounding these random
structures can provide the required amplification when it is properly pumped. Silver
nanowires grown with GLAD techniques can provide very large arrays of nanowires
31
either randomly or periodically, and can act as a feedback system for random nanolas-
ing. The strong scattering from the nanowires provide a high probability of forming
a coherent feedback loop, depending on the length, density, and periodicity (random
or periodic) of the structures.
In order to test the effect that length of the nanowires have on lasing, three dif-
ferent samples were fabricated with different amounts of material deposited (400nm,
700nm, and 1000nm). Due to the growth mechanisms described in the GLAD Fabri-
cation Chapter 2 “Nanowires grown with Glancing Angle Deposition”, we know that
over these deposition thicknesses, the randomly grown nanowires will change from
randomly positioned and sized islands to very short nanowires, and finally to ran-
dom nanowires with strong variation in lengths and structures. Images of the three
fabricated samples are shown in Fig 2.3.
2.4 Experimental Results
The samples were then covered with R6G-PVA (10nM)and pumped using a Nd:YAG
Laser (532nm, 800ps, 1Hz) using an optical setup shown in Fig. 2.4
The output intensity from the 3 different samples were measured and compared
to a glass wafer without any nanowires grown on it. The results can be seen below
in Fig. 2.5a. It is clear that the nanowires greatly enhance the lasing intensity, and
that longer nanowires show a greater enhancement than the shorter wires. To further
demonstrate the lasing effect, the samples were pumped with different powers and
the output intensity was measured. Results from this study can be seen in Fig. 2.5b
These randomly arrayed nanowires clearly show the behavior expected of a lasing
source. There is still ongoing work to determine some of the finer details of lasing in
these structures. First, the lasing could be purely from the strong electromagnetic
field enhancement that these nanowires are expected to exhibit, and not from a co-
herent feedback from the random wires. To completely understand this, simulations
of the structures should be performed to determine the field behavior around indi-
32
Fig. 2.3. Three nanowire samples grown by GLAD with three effectivedeposition thicknesses (400nm, 700nm, 1μm).
vidual and paired nanowires to understand how the field behaves with individual and
paired nanowires. Secondly, the randomly arrayed nanowires should be compared
33
Fig. 2.4. The setup for nanolasing optical measurements
with nanowires of uniform periodicity. Comparing these structures and having strong
simulation results should help us understand more precisely the nature of lasing in
this nanowire sample
2.5 Advanced Nanowire Growth Techniques
While these linearly grown nanowires are interesting, they barely scratch the sur-
face of what is possible with the GLAD system. Another relatively simple nanowire
growth technique using GLAD that would be almost impossible with traditional fab-
rication techniques is a “chevron” nanowire 2.6. For this chevron geometry, the
substrate was rotated 180◦ in the middle of the deposition. After the substrate is
rotated, the continued GLAD deposition will continue growing the nanowires in the
opposite direction. This technique can be repeated several times to create a “zig-zag
nanowire.
If the substrate is rotated by small increments during deposition, a chiral or helical
structure can be fabricated via Glancing Angle deposition. Here the substrate was
rotated 90◦ in 10 small steps while the entire 2μm of silver was deposited. Rather
than depositing the chiral structures randomly onto a flat substrate, Zinc Oxide wires
were grown on a glass substrate by Professor Nicholas Kotov’s student Bongjun Yeom
at the University of Michigan. The ZnO template and the silver nanowires grown on
the template can be seen in Fig. 2.7. Because the deposition of the silver will only
34
Fig. 2.5. a) The intensity spectrum for the 3 nanowire samples com-pared to a blank glass sample. b) The output intensity as a function ofthe input pumping power. Both curves show characteristic behaviorfor lasing
be on the topmost regions of the template (seen in Fig. 2.1), the wires will tend
to grow only on the tips of the ZnO nanowires - acting as a quasi-seeding layer. In
35
Fig. 2.6. “Chevron nanowire - grown by rotating the sample 180◦ inthe middle of the deposition.
this figure, crystalline structure of the silver can be observed along the growth of the
nanowire. While the nanowires grow due to the line-of-sight nature of the Glancing
Angle Deposition, after the material is initially deposited, the atoms will tend to
settle in a crystalline manner, rather than a purely “line-of-sight” fashion.
2.6 Nanowires Grown on a Seeded Template
Like trees randomly growing in a forest, the nanowires previously described will
grow from random locations, and grow to different sizes and geometries. However, by
properly seeding locations for the nanowires to grow, the fabricated structures will be
uniform in period and geometry. This seeding can be accomplished by first creating
a thin film of the material at desired locations on the substrate using traditional
e-beam lithography. However, this seeding method must be approached carefully.
Seeding the wires too closely will cast shadows that prevent neighboring wires from
growing. Seeding the wires too far from one another will allow wires to grow from
36
Fig. 2.7. Silver chiral structures with 90◦ counter-clockwise rotationgrown on a ZnO nanowire template
undesirable locations. Size of the seeding area is also critical as a seeding area that
is too large will allow several nanowires to grow from one location. Seen in Fig.
2.8, a seeded template of Hydrogen Silsesquioxane (HSQ) was made using e-beam
lithography. Here, we see that the silver will grow only from this seeded template,
and not from the flat substrate. The nanowires grown in this fashion are clearly more
uniform in size, shape, and length.
2.7 Complex Nanowires from Previous Literature
Several techniques of Glancing Angle Deposition have been reported in litera-
ture [149–151]. These mentioned papers describe techniques for several advanced
techniques exploiting the GLAD phenomena. While all the structures described above
have been grown with silver on an un-cooled substrate, Glancing Angle Deposition
37
Fig. 2.8. Silver nanowires grown from a seeded template. As thenanowires only grow from the seeded template, their size is moreuniform in size, shape, and length
can be exploited to make nanowires of more complexity by depositing materials will
less surface energy on a cooled substrate. Fig. 2.9 shows several structures made
from MgO on a cooled substrate. This combination allows for nanowire growth of
higher aspect ratios of complex shapes, such as helices and chevron structures.
Fig. 2.9. Various types of nanowire growth via GLAD techniques
38
3. GLANCING ANGLE DEPOSITION ON CURVED AND
SPHERICAL SURFACES
3.1 Introduction
When materials are deposited via PVD on curved surfaces, non-uniform films
can be created. Using Glancing Angle Deposition (GLAD), the line-of-site behav-
ior of physical vapor deposition can be exploited to produce a variety of films with
non-planar geometries for new optical and electrical technologies. This fabrication ap-
proach shows great promise in the Plasmonics and Transformation Optics and meta-
materials community to develop materials with unprecedented control over the flow
of light. A variety of interesting and exciting devices - ranging from non-diffraction
limited lenses to nanolasers can be created using this angled deposition that would
be difficult or impossible to do without this technique.
3.2 Angled Deposition on Curved Surfaces
In physical vapor deposition, the source material will be evaporated in a “line
of sight” manner, and the film deposition thickness is determined (in large part) by
the effective surface area that is exposed to the source material being evaporated. In
the case of a planar substrate, film thicknesses will be uniform because the effective
surface area is constant. However, in the case of a non-planar surfaces, the amount
of deposited material will change with the effective surface area. For example, in the
case of spherical particles, the material deposited at an angle normal to the particle
will receive the full amount of deposited flux, the edges of the particle will receive only
a glancing (close to zero) amount of material, and there will be some distribution in
film thickness across the sphere. An example of the thickness gradient created when
39
a material is deposited at an angle on a sphere is shown in Fig. 3.1. By rotating the
angle of the substrate, an angled deposition can be performed at any angle (between
0◦ and 180◦) over the spherical particle to create this curved distribution of film
thickness from any angle around the sphere.
Fig. 3.1. Schematic of angled PVD deposition on a spherical sur-face. A gradient in thickness is created due to the varying amountsof surface exposed at the angle of deposition
As an example of this film thickness gradient, Fig. 3.2 shows the result of de-
positing 40nm of silver on a 5μm SiO2 microsphere at an angle of 45◦. The growth
dynamics of silver films on SiO2 has been studied in depth and thin film formations
has been previously analyzed. When the effective deposited thickness is below 10nm,
silver will form isolated “islands”. When the effective thickness is around 10nm, the
film will become percolated, and when the effective thickness approaches 20nm, the
film will become continuous. In Fig. 3.2 we see a clear effective thickness gradient
of deposited silver across the microsphere. Because the total deposited film on the
sphere is 40nm, the entire spectrum of this film growth can be seen along the film,
40
from a continuous layer on the upper right (∼20nm), through the percolated film,
islands, and eventually uncoated SiO2.
Fig. 3.2. A 40nm silver deposited at a 45◦ angle over a 5μm SiO2
microsphere. A distribution in effective thickness can be seen rangingfrom no coverage through full continuous coverage.
Multiple layers of different materials can be deposited in this manner to create
“core-shell” structures of alternating materials. By depositing each material at a
large angle (∼ 86◦) and continuously rotating the substrate during deposition, the
outside edges of the sphere will be coated with continuous films, while the top of
the structure will receive a glancing deposition of material. As noted in section 2.2,
nanowires can be grown by depositing the source material at large angles close to 90◦
and care must be taken to prevent these wires from growing at the glancing angles
(top of the sphere). If silver is deposited directly onto SiO2 at large angles, the silver
films will have very rough and discontinuous surfaces, even with larger deposition
41
thicknesses. In Fig. 3.3, five alternating layers of silver and SiO2 are deposited on a
5μm microsphere at an angle of 86◦ without germanium wetting layers. Despite their
relatively large total deposited thicknesses (100nm), the films are extremely rough
and discontinuous. At the top of the structure (Fig. 3.3b), the films are especially
rough due to the shadowing effects occurring at glancing angles (similar to nanowire
growth).
Fig. 3.3. Deposition of silver on SiO2 microsphere without germaniumwetting layer. Despite the films’ relatively large thicknesses, layersare rough and discontinuous. The top of the structure is especiallyrough, due to the shadowed, “nanowire”-like growth of the films atsharp glancing angles
Because of its prominence in the optical community as an outstanding optical
and plasmonic material, great effort has been invested into developing techniques for
depositing silver films as thin as possible. One technique allowing for smooth and
continuous silver film growth on SiO2 is by depositing a very thin (∼ 1nm) germa-
nium wetting layer before the silver. This wetting layer promotes thin and continuous
growth of silver on SiO2 down to thicknesses below 7nm. To create continuous and
uniformly deposited films on spheres, special measures must be taken into account
during deposition. Firstly, the sample must be rotated for a short time to deposit a
small thickness of material over the area of discontinuous growth. Depositing small
amounts of material over these small islands that will form in regions of glancing depo-
42
sition angles will smoothen the regions surface and prevent nanowires from forming.
Secondly, employing a wetting layer (germanium) allows for more smooth films of
silver, which will help with surface roughness and minimize nanowire growth on the
top of these structures. An example of such a core-shell structure can be see in Fig.
3.4. Here, 1nm germanium wetting layers were applied between each silver/SiO2
interface, and the deposition angle was continually changed during the substrate ro-
tation to provide continuous and relatively smooth layer coverage, despite the layer
thicknesses being relatively thin (just ∼13nm)
Fig. 3.4. 1μm SiO2 microsphere before (a) and after (b) FIB cut.Although layers are only ∼13nm each, they remain relatively smoothand continuous
There has been recent interest in the optics community of making non-uniform
layer thicknesses on curved surfaces for devices such as a planar hyperlens and optical
concentrator. By depositing materials at glancing angles onto the microspheres, it
is possible to create films that have a greater thickness on the sides of the sphere
and taper to thin films on the top of the sphere. Fig. 3.5 shows such a sphere
with tapered thicknesses across the side and top of a sphere. These curved layers of
varying thickness can be fabricated by depositing alternating layers of silver and SiO2
at glancing angles (86◦).
43
Fig. 3.5. Gradient film thicknesses around a 5μm microsphere.Fig.3.5a shows the entire microsphere, while Fig.3.5b is an inset ofthe sphere, showing the difference in film thicknesses between the topand sides of the sphere.
3.3 Comments
When growing thin films on curved surfaces, there are several additional notable
effects that must be taken into consideration beyond the purely “line of sight” nature
of the deposition. First, surface diffusion will have an impact on the final structure.
The effects of surface diffusion is nontrivial and depends on several variables, including
the material properties of the deposited material and its underlying layer, substrate
temperature, and deposition rate. While employing germanium as a wetting layer will
improve the growth of silver on SiO2, other parameters (such as substrate temperature
monitoring and cooling) are not available for observation or manipulation in this
system. Secondly, it should be noted that although material can be deposited all
around the outside of the sphere, there will always be an opening at the bottom of
the sphere, where no material can be deposited. This opening can be seen in the
bottom of Fig. 3.5a. Third, only the deposition onto the sphere has been discussed
in this chapter. In practice, deposition on the substrate around the sphere (see, for
44
example Fig. 3.5) is unavoidable and its existence should be accounted for in device
design.
45
4. SHADOWED ANGLED DEPOSITION FOR
THICKNESS TAPERED THIN FILM HYPERBOLIC
HYPERBOLIC METAMATERIALS AND WAVEGUIDES
4.1 Introduction
Typically, in Physical Vapor Deposition (PVD) grown thin films, layers will be
deposited at an angle normal to the substrate, which creates planar films that are
uniform in thickness. However, when a source material is deposited in a PVD evap-
oration at an angle over a mask, a “shadowed” region is created behind the mask.
This region will have a gradient amount of material deposited over the mask, which
will lead to a gradient in film thickness across the substrate. A schematic of this
angled shadowed deposition technique is shown in Fig. 4.1. While this concept may
seem trivial, the ability to create non-planar films of non-uniform thicknesses enables
a new field of nanofabricated devices with a higher degree of control over deposited
films’ thickness. This fabrication technology enables a family of devices with smooth
gradients in electrical and optical properties. This chapter will explain how mul-
tilayered films of alternating metal/dielectric layers can be fabricated with tapered
thickness profiles, and chapter 6 discusses two examples of a device that requires this
fabrication technology.
4.2 Tapered Silver Films on Uniform SiO2
As a source material is deposited at an angle over a mask via PVD, a gradient
in deposited layer thickness can be deposited (Fig. 4.1). The first type of shadow
deposited film described is a multilayered metal (silver)/dielectric (SiO2) structure
46
Fig. 4.1. Depositing material at an angle over a mask will produce ashadowed region behind the mask with a tapered deposition thicknessprofile.
where the silver thickness tapers from 20nm down to 0nm (continuous below 7nm),
and the SiO2 thickness is a constant 58nm across the substrate.
First, a Kapton R© tape mask (∼ 60μm) is applied to the glass substrate before
loading the sample into the chamber. Upon loading the sample , a 1nm germanium
wetting layer is deposited at an angle normal to the substrate (0◦). Next, the sample
is rotated to 20◦, and a 20nm silver film is deposited. By depositing the silver film
at an angle, a “shadowed” region is present behind the Kapton R© tape mask, which
will receive a distribution of deposited material. Regions of the sample that are
more than 20◦ from the top of the tape will receive the full 20nm of deposited silver.
Regions of the substrate below 20◦ will receive a distribution of deposited material.
As a combination of this gradient of flux and surface diffusion, the shadowed region
behind the tape will have a silver film whose thickness tapers between 20nm down to
0nm. SiO2 can then be deposited normal to the substrate to create a film of uniform
thickness (or at an angle to create a film with gradient thickness). The process can
then be repeated many times to create multilayer structures with aligned tapered
thickness films.
47
The length of this tapered region may be increased by rotating the angle of flux
during the deposition. For example, holding the substrate at 20◦, but sweeping ± 2◦
will increase the length of the tapered region of the film. Fig. 4.2 shows layers of
silver tapering in thickness from 20nm down to zero, while the SiO2 layer thicknesses
remain constant at 58nm. Here, 45 layers in total were deposited (15 each of SiO2,
Ge, and Ag).
Fig. 4.2. Alternating metal / dielectric layers with subwavelength thickness
4.3 Tapered SiO2 films on Uniform Silver
While the previous section described a technique for creating a gradient films with
thicknesses tapering down to zero, here focus is on continuous films with non-planar
and non-uniform thicknesses. Rather than tapering the thickness of the silver film,
the SiO2 thickness is tapered in this case. Using similar angled deposition techniques,
these films may also be realized.
By adjusting the thickness of one material (dielectric), while keeping the thickness
of the other material constant, the effective properties of the composite material vary
with their relative filling fraction. The fabrication of this class of material begins
similarly, with a mask over which the materials are deposited. In this case, each
material is first deposited at a normal angle (0◦) to the substrate. After the desired
48
thickness for one part of the structure (thickness 1) is achieved, the deposition angle is
rotated, creating a shadowed region with tapered thickness. The material continues to
be deposited at this angle until the final thickness of the second part of the structure
(thickness 2) is achieved. Through these means, a two (or more) sectioned effective
metamaterial can be fabricated with smooth transitions between sections. Fig 4.3
shows such a fabricated structure. Here, there are 15 layers each of silver and SiO2
(with 15 germanium wetting layers). The silver films here have a uniform thickness
of 10nm across the entire structure, while the SiO2 thickness varies between 30nm
and 100nm. This change of thickness changes the metal filling fraction, which in turn
changes the effective permittivity of the material in the in-plane and out-of-plane
directions.
Fig. 4.3. 15 alternating silver/SiO2 layers. Each silver layer has auniform thickness of 10nm. Each SiO2 layer has a thickness thattapers between 30nm and 100nm
The strong change in metallic filling fraction across the substrate is enough to
make the material’s in-plane permittivity an effective positive (dielectric) at one side
(thick) of the structure, and an effective negative permittivity (metal) on the other
(thin) side of the structure. This strong change in effective optical properties of the
film have very interesting properties for a field or wave passing along this adiabatically
tapered film.
49
4.4 Planar Magnifying Hyperlens
One exciting application for the fields of Transformation Optics and metamaterials
is to develop devices with resolution less than the diffraction limit. Feature sizes less
than the diffraction limit have their spatial information contained in waves with large
wave vectors or k-vectors. Because normal dielectric materials (such as air, glass, etc.)
only allow waves with finite (and relatively small wave vectors) to propagate through
them. In contrast, hyperbolic metamaterials (HMMs) do allow large k-vectors to
propagate through them. While the large k-vectors can propagate inside the HMM,
they cannot propagate through air, as the high-k waves are evanescent, and lost in the
far-field. Rather than using planar HMM layers, the layers can be curved to magnify
the image of the object. If there is enough magnification to bring the feature sizes
of the object larger than the diffraction limit, the features can indeed propagate into
the far-field, where they can be detected through conventional optical techniques.
Therefore, a magnifying hyperlens can provide resolution much below the diffraction
limit in the far-field. While a magnifying hyperlens has been demonstrated using a
curved, cylindrical structure, there remains a desire to have a hyperlens that is planar,
such that it can be more easily integrated with conventional optical microscopes.
For this reason, we have developed a metamaterial that has hyperbolic dispersion
(to allow high-k waves to propagate), curved on one side (to provide the required
magnification), and planar on the other side (to easily integrate into conventional
optical systems).
4.5 Design and Fabrication
As discussed previously in Section 4.3, a wedge-like structure can be fabricated
that is hyperbolic, curved on one side, and planar on the other side. As the curvature
of the layers will determine the device’s magnification, the curvature should be as
large as possible. As can be seen in Fig. 4.3, the final curvature (and magnification)
of the structure will become larger as more curved layers are consecutively stacked
50
upon one another. Unfortunately, because the metal (silver) used in the HMM is
lossy, more added layers will lead to more loss. Therefore, there is a direct tradeoff
in this structure between magnification and internal losses (depending on the metal
used).
4.6 Simulations and Remarks
While this fabrication technique of making the curved wedge structure does pro-
vide magnification, limitations in the fabrication process dictate the limitations of the
final curvature of the structure. Because the structure in Fig. 4.3 is the largest cur-
vature achievable with this technique, we used this structure to simulate the amount
of achievable magnification. Using a COMSOL FEM model, the HMM structure was
simulated with two slits in a chromium (used for blocking the light) mask. Here, the
two slits are separated by a distance of 1100nm. One of the slits is on the flat region,
where the feature will travel straight through the structure, while the other slit is
positioned on the curved part of the structure, where its features will be magnified.
The image is detected in the far-field, and the magnification can be defined as the
ratio between the separation of the two slits, and the separation of the two intensity
peaks detected in the far-field. Upon simulating this structure, the results can be
seen in Fig. 4.4.
These simulations are useful, but unfortunately do not provide the results we
hoped for. On one side of the wedge, the two slits are separated by 1100nm. Upon
passing through the HMM wedge structure, the separation in intensity peaks is ap-
proximately 1300nm. While there is some magnification, it is only a factor of about
1.18, or 18% larger. As previously mentioned, adding more layers to this structure
would indeed increase the magnification, unfortunately, it would also provide greater
losses, to which this device is already very sensitive. In conclusion, while this de-
vice does, in principle demonstrate magnification is possible, the magnification is
not nearly enough to be useful in a practical device. However, using metallic films
51
Fig. 4.4. Simulations used to calculate the magnification induced fromthe HMM wedge structure.
with lower losses would allow one to increase the number of layers used, which could
provide the greater curvature needed for a planar magnifying hyperlens.
52
5. INTRODUCTION TO HYPERBOLIC
METAMATERIALS
Bulk materials have a dielectric permittivities ε(λ) = (ε′ + iε′′). While the real part
of the dielectric function (ε′) describes the strength of the polarization induced by
an external electric field, the imaginary part (ε′′) describes losses associated with the
materials electric response. Metals (by definition) have a negative ε′, due to their
free-electron behavior at the wavelength of operation, while dielectric materials have
(by definition) a positive ε′. By stacking alternating layers of metal and dielectric
with subwavelength thicknesses (Fig. 5.1), this “metamaterial” exhibits effective
permittivities in the in-plane and out-of-plane directions, which can be approximated
by Effective Medium Theory (EMT). Here, the permittivity in-plane (x-y, or ε‖) can
be approximated by Eq.(5.1), the out-of-plane permittivity (ε⊥) can be approximated
by (5.2), and the relationship between k-vectors in the 3 directions is described by
Eq. (5.3).
Fig. 5.1. Alternating metal / dielectric layers with subwavelengththickness and coordinate system used.
ε‖ = fmεm + (1− fm)εd (5.1)
53
ε−1⊥ =
fmεm
+1− fm
εd(5.2)
k2x + k2
y
ε⊥+
k2z
ε‖=
(ωc
)2
(5.3)
In these equations, εm is the real part of the permittivity of the constituent metal
layers, while εd is the permittivity of the dielectric layers. The variable fm is the volu-
metric metal filling fraction, ε‖ is the permittivity in the in-plane (x and y) directions,
and ε⊥ is the permittivity in the out-of-plane (z) direction. One can see from these
equations that as the metal filling fraction is increased, the effective permittivities will
eventually become negative. In the range where the in-plane permittivity is negative
and the out-of-plane permittivity is positive, the dispersion relation between ky and
kz will exhibit a hyperbolic profile. One-quarter of a cross-section of the dispersion
relations for air, SiO2, and an HMM are shown in Fig. 5.2.
Fig. 5.2. Dispersion relations for air, SiO2, and an HMM structure,demonstrating how waves propagating in the z-direction cannot becoupled to air or SiO2 because the y-components of the wave vectorscannot be matched.
54
Simple dielectric materials, such as air and SiO2, have ellipsoidal (or spherical)
dispersion relations. Waves propagating in these media have relatively small wave-
vectors that are bound to their dispersion curves. The name “Hyperbolic Metamate-
rial” comes from the shape of the dispersion profile for this class of materials, which is
a hyperboloid as shown in Fig. 5.2. The hyperbolic dispersion relation illustrates how
an HMM can support unbounded k-vectors that can be extremely large in magnitude.
For these reasons, HMMs have been of great interest to the optics community, and
have been used for several devices with unprecedented optical performances. The
resolution of conventional optical systems is limited by the Abbe diffraction limit.
In these systems, the resolution is limited by Eq. (5.4). Feature sizes smaller than
d have large k-vectors that will evanescently decay in media that cannot support
the large-k wave vectors. Because HMMs do support large k-vectors, subwavelength
features are preserved when traveling through the HMM. By curving the planar HMM
layers into a cylindrical structure, the features can be magnified to sizes above the
diffraction limit and these low-k waves can propagate into the far-field. In this way,
sub-diffraction limited features can be imaged in the far-field - a device known as a
hyperlens.
d =λ
2nsin(θ)(5.4)
As the photonic density of states (PDOS) is proportional to the volume of the
shell enclosed between two isofrequency contours in the k-space, HMMs can have a
PDOS that is much greater than that of dielectric media. An emitter’s spontaneous
emission is determined by the surrounding material’s PDOS. An HMM can provide
a coupled emitter with a nearly infinite broadband set of additional decay channels
that can ultimately enhance the emitters spontaneous emission through the Purcell
effect. Because the PDOS is proportional to the maximum k-vector in the surrounding
medium cubed (PDOS ∼ k3max), every small increase in the maximum wave-vector
in the system can lead to a drastic enhancement of the PDOS. This approach has
produced valuable results towards improving the efficiency of broadband single pho-
55
ton sources (such as Nitrogen Vacancy centers in nanodiamonds) [152]. However,
the high-k modes, which are evanescently coupled into the HMM are very difficult
to outcouple, due to a very large momentum mismatch. The next Chapter 6: “Ta-
pered Hyperbolic Metamaterial Waveguides” is devoted to designing, simulating and
fabricating a device that drastically enhances an emitter’s PDOS, and provides an
efficient method for outcoupling the high-k waves.
56
6. TAPERED HYPBERBOLIC METAMATERIAL
WAVEGUIDES
6.1 Introduction
Due to the extremely large Photonic Density of States (PDOS) of HMMs, they
have the potential for drastically enhancing the spontaneous emission rate of single-
photon emitters. Using HMMs for enhanced single-photon emission has been previ-
ously studied [152], and a two-fold increase in emission rate was measured by placing
the single-photon emitters in close vicinity to a TiN/AlScN structure exhibiting hy-
perbolic dispersion. While placing the emitters above an HMM clearly enhances the
emission rate of single-photons, the enhancement goes into high-k waves of the HMM
and cannot be detected in the far-field. One proposed method for extracting the
high-k waves from the HMM is by surrounding the emitter by a “bulls-eye” grating
structure [153]. This technique should be avoided as it is narrow-band, and does not
take full advantage of the broadband nature of HMMs.
6.2 Outcoupling High-k Waves from HMMs
One of the distinguishing characteristics of HMMs is that they support propa-
gation of high-k waves. However, the challenge in taking full advantage of these
materials is the extracting (out-coupling) these high-k waves into free space. Fig.
6.1a illustrates this problem. For a wave incident on a material in the z-direction, the
in-plane (x- and y-component) of the field must be conserved. It is therefore impossi-
ble to couple light between the HMM and air or SiO2, as the k-vector cannot transfer
between the materials while conserving ky (Fig. 6.1). A wave at this HMM/dielectric
interface will be evanescent, and quickly decay.
57
In contrast to waves propagating in the z-direction, waves propagating in the y-
direction must conserve the z-component of the k-vector. In this case, it is possible to
couple light between HMMs and dielectrics such as air and SiO2 while preserving the
z-component of the wave-vector. In figure 6.1a, we can see that coupling is possible
when the magnitude of the z-component of the wave is less than that shown in the
green dashed line.
Typically, dielectric materials and HMMs are classified as two distinct material
groups. However, here we examine the behavior of these metamaterials as they tran-
sition between dielectric and HMMs by varying the constituent metal filling fraction.
Figure 6.1b shows the dispersion relation for HMMs of different metallic filling frac-
tions, ranging from 0% (pure dielectric) to 35% (clearly HMM). This figure assists
in the understanding of waves propagating in and between metamaterials of different
metallic filling fractions.
For waves propagating along the HMM in the in-plane (y) direction, the kz com-
ponent of the field must be conserved. As the field traverses between materials, the
k-vector will pass between dispersion curves in a horizontal manner, as shown in Fig.
6.1b. From this figure, it can be seen that wave vectors transform from k3 to k2 as
the metal filling fraction changes between 23% and 35%. The wave vector can also
transform from k2 to k1 as the wave passes from the HMM with 35% filling fraction
into air (along the green line in Fig. 6.1b). It is possible for wave vector k3 to directly
convert into k1, however, this coupling transition will have higher reflective losses (as
reflection is determined by the difference in magnitude of k-vectors).
While extracting light from the HMM into air is clearly important, the enhance-
ment of the PDOS must also be analyzed. The enhancement of the PDOS is propor-
tional to the cube of the maximum k-vector of the surrounding HMM (k3max). Wave
vector k3 is larger in magnitude than k2 and will have a significantly larger enhance-
ment of the PDOS. Likewise, k2 will have a significantly enhanced PDOS compared
to k1. While considering the possibility of using these single photons in a practical
device however, outcoupling these high-k waves must be considered. While k3 shows
58
greater enhancement, outcoupling the enhanced modes of vector k3 into free space
is very inefficient due to the large wave vector mismatch between k3 and k1. Con-
versely, vector k2 has better coupling efficiency to k1, but a much lower enhancement
of PDOS (compared to k3). Ideally, one would like a metamaterial waveguide that
can exploit the benefits of both filling fractions of HMMs. This can be accomplished
with a waveguide where one end would have a maximum enhancement of PDOS, and
the other end of the waveguide would have optimal coupling between the HMM and
free space. Between the two HMMs, a smooth transition would provide a medium
for the large k-vectors to be converted into low-k vectors while eliminating reflective
losses by adiabatically tapering the metal filling fraction of the HMM.
While a tapered waveguide can be designed to optimize the outcoupling of high-k
waves into free-space, these structures can also be used to quench the high-k modes
traversing through a tapered waveguide. In the previous example, high-k waves are
first created in the HMM region of lower metal filling fraction, and are converted into
lower-k modes as they pass into the HMM with higher metal filling fraction. By using
the waveguide in a reverse manner and decreasing the metal filling fraction (greatly
increasing the magnitude of the wave vector), high-k waves of an HMM can be quench.
By introducing high-k waves into the HMM in a region of high metal filling fraction,
the waves can pass along the waveguide into a region with lower metal filling fraction
(eg. from vector k2 to k3 in Fig. 6.1b). In this case, the magnitude of the k-vector will
grow very quickly into very high-k modes, where the energy will quickly be quenched
as the metal filling fraction approaches zero.
The goals of this work is to demonstrate that high-k waves can be coupled out of
HMMs, and finally, to demonstrate a waveguide that can optimize both enhancement
of PDOS, and outcoupling into free-space. Using a similar design, a parallel goal is to
demonstrate an adiabatically tapered waveguide with decreasing metal filling fraction
will quench the high-k waves passing through.
59
Fig. 6.1. Dispersion relations for various dielectric and HMM struc-tures. Fig. (a) demonstrates how waves propagating in the z-directioncannot be coupled to air or SiO2. Waves propagating along the y-axiscan be coupled to SiO2 or air, as they have matching z-components oftheir respective wave-vectors. Fig. (b) shows how the dispersion rela-tion for various dielectric and HMMs change as a function of metallicfilling fraction.
6.3 Design
From of Fig. 6.1b, it is evident that HMMs with lower filling fractions are better
for supporting and propagating very high-k waves, while HMMs with higher filling
60
fractions will couple into free-space more efficiently. The design for the adiabatically
tapered HMM waveguide will therefore proceed as follows: First, an HMM is chosen
with a metal filling fraction for an optimized enhancement of the PDOS. The emitting
source should be place in this region to optimize the source’s emission enhancement.
When choosing the filling fraction of this HMM, It is critical that the kz component of
the field one would like to outcouple must lie below the kz component of the material
of which the wave will eventually be outcoupled (shown as the green dashed line in
Fig. 6.1b). Next, an HMM with a different metal filling fraction is chosen which
has ky components that will be outcoupled as close to the surrounding dielectric as
possible. The purpose of the HMM in this region is to minimize reflection between
the HMM and the surrounding dielectric, which is satisfied when the k-vectors of two
regions are matched as closely as possible. Finally, the two regions of the HMM will
be joined by an adiabatically tapered waveguide structure.
The tapering of this waveguide allows the large k-vectors (e.g. k3) to smoothly and
efficiently transition into smaller k-vectors (e.g. k2) through an impedance matched
region that will minimize reflection. The length of the tapered transition should be
larger than the operating wavelength to avoid abrupt transitions (large reflections),
while not being too long - as material losses in the constituent metal will decrease the
device’s internal efficiency (the length would be on the order of 1μm). The number
of layers deposited in the structure should be at least 5 (of each Ge/Ag/SiO2) so that
the structure behaves as an HMM, although the number of layers can be increased
if the desired size of the outcoupling end of the waveguide is required to be larger.
The waveguide should be abruptly truncated at the end of the tapered region on the
outcoupling side to avoid unnecessary losses. The emitter should be place on top of
the HMM with optimized enhancement of the PDOS (e.g. k3), and as close as possible
to the tapered region. The enhanced emission will travel into this HMM, through the
adiabatically tapered waveguide, and outcoupled into air (or other dielectric medium)
with maximized outcoupling efficiency (as seen in Fig. 6.2b).
61
Fig. 6.2. Outcoupling of enhance emission of single-photon emitters
For the case of quenching in tapered HMM waveguides, the design should be
reversed. Rather than designing the waveguide’s dispersion relation to transform
high-k waves into low-k waves to be outcoupled, for quenching, the high-k wave
should be transformed into very high-k waves that cannot couple into free-space and
will quickly die in the tapered region of the waveguide. In this case, as the waves
move along the tapering of the waveguide, the metal filling fraction should taper
down to zero. In practice, this tapering can happen in two ways: First, the metal
film thicknesses can decrease down to zero. While in practice it is very difficult to
bring the thickness of a silver film perfectly down to zero, the films can certainly be
continuous below 7nm, which can correspond with a very low metallic filling fraction.
The second option is to increase the dielectric film thickness while leaving the metal
thickness the same - which also decreases the metal filling fraction. Similar to the
outcoupling structure, the length of this tapered region should also be larger than the
wavelength to avoid abrupt transitions in the waveguide and prevent large reflections.
A schematic for the quenching tapered waveguide is shown in Fig. 6.3 where the metal
film thickness tapers down to zero.
6.4 Simulations
Using a commercial Finite Element Method (FEM) software package (COMSOL
Multiphysics), multilayer HMM structures with different metal filling fractions were
simulated to find how well waves in HMMs outcouple to air. For both the simulated
62
Fig. 6.3. Quenching of high-k waves passing through metamaterialwith decreasing metallic filling fraction
structures shown in Figure 6.4, the scatterers (at equal distances from each end of
the waveguide) are cut adjacent to the tapering. In Figure 6.4a, the modes propa-
gating along the tapered region clearly encounter significant propagation loss as the
magnitude of k increases with the decreasing metal filling fraction. Thus, device 1 is
a possible solution for efficient light absorption (i.e. in-line waveguide termination).
Alternatively, the design 2 simulation reported in Figure 6.4b predicts the possibility
of tapering to convert the high-k HMM modes into waves with lower-k which can out-
couple more efficiently into air. The power outcoupled from the tapered HMM section
(right of Figure 6.4b) into air is 10% larger than the power outcoupled from the non-
tapered HMM (left Figure 6.4b). Additionally, the final filling faction of design 2 can
be further optimized to maximize the outcoupled power for a certain range of high-k
modes. Design 1 has been tested to verify the feasibility of in-plane out-coupling,
and design 2 is still under investigation to confirm the predicted improvement of the
outcoupling efficiency
As expected, the outcoupling efficiencies are greater when the magnitude in k-
vectors across the HMM/Air interface match more closely (see Fig. 6.1b). From
the chart in Fig. 6.1, the HMM with 35% metal filling fraction clearly has the
highest outcoupling efficiency and should be used to outcouple from the HMM to
air. However, although the HMM with 35% metal filling fraction provides the best
63
Fig. 6.4. Outcoupling efficiencies of HMMs with various metal fillingfractions (a). Simulated outcoupling for one of the more high-efficientmodes (b).
outcoupling, the magnitude of the k-vector in this HMM is not nearly as large as that
of the HMMs with lower metal filling fractions, and will therefore have a much lower
enhancement in PDOS.
6.5 Fabrication
The fabrication process for these tapered waveguide structures is explained in
greater detail in Chapter 4.3, but a brief description specific to the design above
is presented here. First, a (∼ 60μm) Kapton R© tape mask is applied to an SiO2
substrate before loading the sample into the chamber. Upon loading the sample into
the evaporation chamber, a very thin (∼1nm) germanium wetting layer is deposited
followed by a 16nm silver layer at a normal angle of incidence. Next, SiO2 is deposited
normal to the substrate until the thickness is 30nm (corresponding with a 35% metal
filling fraction). The substrate is then rotated 20◦ and the SiO2 continues depositing
until the final thickness is 48nm (corresponding with a 25% metal filling fraction).
Rotating the structure during the deposition will create a shadowed region with a
64
tapered thickness profile that transitions between the two HMM regions. The steps
for depositing the three materials should be repeated until the final total number of
layers is deposited. A schematic for this fabrication procedure and final fabricated
structure (although with different filling fractions) can be seen in Fig. 6.5
Fig. 6.5. Outcoupling of enhance emission of single-photon emitters
The fabrication method for creating the quenching tapered waveguide can also be
fabricated using an angled deposition technique. First, a (1nm) germanium wetting
layer should be deposited normal to the substrate. This wetting layer is crucial
when tapering the silver film, because without it, the silver will not be continuous
for thicknesses below 20nm, and the films will be rough and non-continuous as the
metal filling fraction decreases. For creating the tapered structure where the silver
film thickness tapers down to zero, the silver film can be deposited over the KaptonR©
tape mask - providing a shadowed region that will create a region of tapered film
thickness. The thickness will taper down from 20nm in the more metallic HMM
region, down to 0nm in the fully dielectric region. After each silver layer, SiO2 will be
deposited at an angle normal to the substrate to create SiO2 films which are uniform
65
in thickness. Because the metal film thicknesses taper down to zero, and the SiO2
thicknesses are constant, the metal filling fraction will taper from an HMM to a pure
(SiO2) dielectric. A fabrication schematic and SEM image of the final quenching
tapered HMM waveguide can be seen in Fig. 6.6.
Fig. 6.6. Outcoupling of enhanced emission of single-photon emitters
6.6 Conclusions
While HMMs provide a medium with extraordinary fundamental optical proper-
ties (including extremely high PDOS), HMMs have until this point, remained elusive
for use in practical devices because their extraordinary optical properties are diffi-
cult to observe in the far-field. These properties (including enhanced emission from
single photon emitters, and super-resolution) are contained within high-k waves that
can propagate within HMMs, but evanescently decay in dielectric media (which have
bounded k’s). To this point, methods for converting these high-k waves into the far-
field have been impractical and inefficient. Here we propose a design for outcoupling
66
broadband high-k waves from an HMM with relatively high efficiencies. Rather than
outcoupling in the out-of-plane direction, high-k waves can be converted into low-k
waves in the in-plane direction. Furthermore, the enhancement of the PDOS and the
impedance matching for outcoupling can be independently optimized by using HMMs
of different filling fractions. These HMMs can then be linked by a tapered transition
region, which converts high-k waves into low-k waves (or vice versa) with impedance
matching for reduced reflection. Most importantly, this technique allows for both an
optimized enhancement in PDOS and optimized outcoupling of the high-k waves into
free-space.
67
7. ALL-DIELECTRIC FULL-PHASE CONTROLLED
METASURFACES
7.1 Introduction
Controlling and manipulating the phase of an electromagnetic (EM) wave is a
fundamental technique in optics and optical devices. While there are devices which
currently serve this purpose, there remains a need for optical devices that are smaller,
thinner, more efficient, broadband, and in many cases, Complementary Metal Oxide
Semiconductor (CMOS) compatible.
Recently, researchers have expanded the knowledge of controlling the phase of
light at a planar boundary - leading to a modification of Snell’s Law (one of the most
fundamental laws in optics) [154]. Most of the related work in this field involves
altering the phase of an incident wave at the boundary of two dielectric materi-
als by using arrays of plasmonic (metal) antennas with different geometries, which
have a plasmonic response, leading to discrete phase discontinuities. This new field
has recently gained attention in the metamaterials community, and many various
demonstrations have been conducted, including a focusing lens [155], extraordinary
reflection/refraction [154], three-dimensional holograms [156], waveplates [157], bire-
fringence [158] and others.
While these various devices have been shown to function, they rely on plasmonic
surface structures, which suffer from high losses, and very low efficiencies (currently
10% or below in transmission mode [157]), especially at optical and infra-red frequen-
cies. Additionally, these metasurfaces only work for specific input polarization, and
very specific antenna design to achieve the required phase distribution.
To this end, the phase (or wavefront) and polarization of incident light can be
modulated by using metasurfaces - specifically designed, subwavelength metamate-
68
rial structures on a substrate’s surface. Metasurfaces are designed to abruptly and
precisely shift the phase, amplitude or polarization of incoming light. Metasurfaces
are able to fully control the phase within a thin layer (less than the free-space wave-
length) after transmitted through, or reflected by the metasurface. These optically
thin metasurfaces are desired over 3-Dimensional (3-D) optical materials, due to their
relatively simplistic fabrication, and reduced thickness. Existing metasurfaces rely
on plasmonic (metal) structures to achieve the desired phase shift. These structures
depend on a plasmonic resonance, making them inherently lossy and narrowband.
In contrast to plasmonic metasurfaces, dielectric metasurfaces completely eliminate
losses within the metasurface, greatly improve efficiencies, and operate broadband, all
while remaining very thin - less than one free-space wavelength. Furthermore, these
binary structures can all be fabricated simultaneously with a single lithography and
etching process.
7.2 Detailed Description
In contrast to existing metasurfaces, all-dielectric, subwavelength, lossless, meta-
surfaces with full (2π radians) phase control, and much higher efficiency have been
developed. These surfaces are also very thin (less than the wavelength of light in free-
space). Additionally, because this technology is not reliant on any resonant effects
(such as plasmonic or phononic), the phase modulation is broadband. In this chapter,
dielectric is defined as a material with positive real-part of permittivity (ε′) at the
operation wavelength that does not exhibit a metallic (plasmonic) response, and this
definition does include semiconductors such as silicon. Similar to plasmonic meta-
surfaces, dielectric metasurfaces can still be very thin - smaller than the free-space
wavelength.
69
When a plane wave is incident on the boundary of two dielectric materials with a
”step”-like geometry as shown in Fig 7.1, the phase of the wave will shift by a phase
given in Eq. (7.1) [159]
Δφ =height× 2πΔn
λ0
(7.1)
where λ0 is the wavelength of incident light in free space, Δn = nhigh − nlow where
nhigh is the material with high index, and nlow is the surrounding medium with low
index. In order to achieve full phase control (Δφ = 2π), the height (or depth) of
these various structures should be at least (7.2)
height =λ0
Δn. (7.2)
For example, if the substrate is Silicon (nsilicon = 3.48) surrounded by air (nair =
1.00), the metasurface thickness should be at least 626nm for 1.55μm incident light.
In other words, having an abrupt step in height of one material can bring an
abrupt change in phase Δφ of 2π. However, what is desirable for most applications is
the ability to have full control over phase modulation (any angle between 0 and 2π)
at any location on the metasurface, as shown in fig 7.1
Fig. 7.1. The figure on the left shows an abrupt change in height,resulting in a 2π phase shift. The figure on the right shows a gradienttransition from nlow to nhigh, providing any phase between 0 and 2π
In order to achieve this, a family of discrete, dielectric metamaterial structures
that exhibit an abrupt change in phase of any angle between 0 and 2π has been
70
developed. These structures are broken down into two groups: posts and holes, with
all structures having approximately the same height (or etching depth). In various
aspects, when the minimum height from Eq. (7.2) is achieved, control over the full
Δφ = 2π phase control is possible, leading to a large number of new applications.
The period of these dielectric elements should be less than or equal to approxi-
mately(7.3)
period ≤ λ0
nhigh
(7.3)
to behave as an effective metamaterial and avoid higher-order modes, and therefore
scattering.
Here, posts refer to solid high-index dielectric elements surrounded by low-index
medium, and holes are a high-index medium filled with ”holes” of the low-index
medium. As the size of the posts increases (or size of holes decreases), the filling
fraction of high-index material increases, increasing the phase delay caused by the
metasurface. Additionally, structures that are entirely high-index or low-index ma-
terials (neither holes nor posts) can be used. The size of posts and holes can be
precisely modulated, allowing almost any sized hole or post to be fabricated (only
limited by fabrication methods and periodicity from Eq. (7.3)). Using this precision,
structures with a smooth gradient in size can be created.
The geometry and filling fraction of each structure changes the phase differently,
producing a smooth gradient and large distribution in phase for variously sized posts
and holes with vertical sidewalls. Figure 7.3 demonstrates one example - using silicon
and air as high- and low-index materials (respectively), equation (7.2) defines the
minimum height for full-phase modulation to be 626nm when the incident wavelength
(λ0) is 1.55 μm. Using a slightly larger height of 650nm, simulations show that a phase
difference (Δφ) of more than 2π can be achieved. The various structures have been
modeled and their reflections have been calculated to be between 0.4% and 30%.
One significant difference between these dielectric metamaterial structures, com-
pared to their plasmonic counterparts [154] is the drastic improvement in efficiency.
71
Fig. 7.2. Periodic arrays of 4 different dielectric metasurface elementtypes (a) Large Posts, (b) Small Posts, (c) Large Holes, (d) SmallHoles. Each element type has a corresponding phase accumulationassociated with it. In general, the phase shift corresponds with thefilling fraction of high-index to low index materials in the structures.Generally, (a) - (d) corresponds with the phase accumulation fromleast to greatest. In addition to these 4 structures, purely low-index,or purely high-index elements can be implemented - correspondingwith smallest and largest phase displacement (respectively).
Because these structures do not require a metal (plasmonic) response, they are nei-
ther subject to the inherent losses in metals, nor do they depend on any resonance -
making them broadband. In fact, these dielectric structures have virtually no losses.
The metasurface can be designed to be either dependent or independent of polariza-
tion. Furthermore, these structures can have a reduced impedance mismatch between
planar high-index to low-index interfaces, which can lower reflections and increase
throughputs if desired. Even lower reflections can be achieved by creating structures
with non-vertical tapered sidewalls, further reducing the impedance mismatch.
72
Fig. 7.3. Phase displacement corresponding with various post / holestructures. Posts and holes on the bottom are schematic sketches ofholes and posts of different sizes
7.3 Anomalous Refraction with Dielectric Metasurfaces
Applications for these dielectric metasurfaces include any optical element that
utilizes 2π (or close to 2π) phase modulation. Just a few applications this technol-
ogy is applicable towards include wave-plates, aberration free lenses, spatial light
modulators, photonic computing devices, polarization dependent & independent ex-
traordinary reflection & refraction, improved Total-Internal Reflection (TIR) cou-
pler/decoupler, optical vortexes, wavefront shaping, beam shaping, 3-D full-wave
Holograms, integrated optics, tunable, adaptive & tunable optics, birefringence, dis-
play technologies, energy harvesting, photovoltaics, and many others. The remaining
part of this chapter is devoted to extraordinary reflection and refraction (as seen in
Fig. 7.4)
73
Fig. 7.4. Extraordinary refraction arising from the distribution inphase accumulation along the dielectric metasurface. The top figureshows one unit cell of the extraordinary reflection / refraction array.The bottom figure shows a beam entering a metasurface and under-going extraordinary reflection or refraction. A similar approach canbe taken for reflecting light at extraordinary angles.
One example of using dielectric metasurfaces to modulate the phase and direct
the direction of incoming light is a blazed grating structure. Operating at 1.55μm,
such silicon post and hole structures can refract incoming light anomalously.
As previously discussed, a series of binary post/hole structures can be used to
linearly alter the phase of the transmitted light by increments of 2π by altering the
structures filling fraction of high-index and low-index materials
The array of post structures were fabricated in the following manner (schematic
in Fig. 8.3). First, a 500μm × 500μm array of square and square-with-hole structures
were patterned into AEP resist on a double-side-polished (DSP) wafer. These pat-
terned structures are for the mask for the host and hole structures. Next, a 45nm layer
of Al was deposited in a standard deposition and lift-off procedure. This Al Layer was
74
used as the mask for later etching. Etching was performed on these structures using
the Panasonic Reactive Ion Etcher (RIE) with SF6 gas. In total, 4 consecutive etches
were performed on the structure. In between each etch, the sample was examined in
the SEM, and the bias power in following etching recipes was adjusted to maintain
vertical walls through the etching process. After the final etching depth was achieved
(∼600nm), the remaining Al mask was removed with “NanoStrip” (Piranha) and the
final structures can be seen in Fig 7.6
Fig. 7.5. Schematic showing the major steps of the fabrication process.
Fig. 7.6. Sideview of the post and hole structures fabricated foranomalous refraction.
75
Here, we see that indeed the binary dielectric metasurface layer does refract light at
anomalous angles very efficiently. While only 6.2% of light travels straight through the
sample, as predicted by traditional Snell’s law, 46.8% refracts at an anomalous angle
(calculated), and 33.88% exits the sample at an anomalous angle of 23◦ (measured).
Angular measurements of the sample were taken using the spectroscopic ellip-
someter. Focusing probes were used to focus the incident light down to a 500μm
diameter. The sample was illuminated normal to the substrate on the etched side
of the sample. Transmission measurements were taken by sweeping the detector be-
tween -5 and 30◦ from the substrate normal. Measurements at 1.55μm were taken
with both p-polarization (along the surface gradient) and s-polarization (perpendic-
ular to the surface gradient). The results are shown below in Figure 7.7. While the
structure was designed to operate at 1.55μm, the optical transmission was measured
in a broadband range from 1μm to 2.3μm. As expected, the silicon absorbs light with
wavelength below ∼ 1.2μm, and anomalously refracts light at a very broad range of
wavelengths at a range of angles very efficiently, as can be seen in Fig. 7.8.
Upon this first demonstration of refracting light at anomalous angles, these same
principles are applied in the Chapter 8 “All-Dielectric Metasurface Focusing Lens”
for creating a dielectric metasurface focusing lens.
76
Fig. 7.7. Angular transmission measurements at λ = 1.55μm.
77
Fig. 7.8. Spectroscopic angular scan of the transmission through thesilicon metasurface for p-polarization (Results are almost identical fors-polarization).
78
8. ALL-DIELECTRIC METASURFACE FOCUSING LENS
We have proposed, designed, manufactured and tested low loss dielectric micro-
lenses for infrared (IR) radiation based on a dielectric metamaterial layer. This meta-
material layer was created by patterning a dielectric surface and etching to sub-micron
depths. For a proof-of-concept lens demonstration, we have chosen a fine patterned
array of nano-pillars with variable diameters. Gradient index (GRIN) properties were
achieved by engineering the nano-pattern characteristics across the lens, so that the
effective optical density of the dielectric metamaterial layer peaks around the lens
center, and gradually drops at the lens periphery. A set of lens designs with reduced
reflection and tailorable phase gradients have been developed and tested - demon-
strating focal distances of a few hundred microns, beam area contraction ratio up to
three, and insertion losses as low as 11%.
79
8.1 Introduction
Flat and compact micro-lens arrays can be used for many applications including
imaging systems, displays, and detectors. In contrast to conventional curved lenses
and lens arrays, dielectric metasurface lenses can be readily wafer-level integrated and
manufactured using processes compatible with CMOS technology. These lenses can
be designed to improve the effective array filling factor by being tightly mapped on a
surface. Size, weight, and other packaging characteristics for optical sensors, as well
as assembly cost, can be improved significantly. Making binary surface GRIN lenses
as a metamaterial layer can be more efficient, compared with conventional methods
of micro-lens manufacturing (such as surface profiled Fresnel lenses, geometric micro-
machined lenses, or an assembly of separate discrete micro-lenses into arrays).
Planar binary surfaces with sub-wavelength patterns have been used for reducing
the reflection [160] from high index materials, as well as modulating the phase [161]
of the transmitted wave. While this phase modulation can be accomplished using
plasmonic surfaces, dielectric metasurfaces have the huge advantage of reducing or
even eliminating insertion losses. Strong intrinsic absorption within an operational
spectral band located in the vicinity of the plasmonic resonances results in very low
transmission through plasmonic metasurfaces, at a level of a few percent at best.
This makes the plasmonic approach impractical for transmission optics applications.
Conversely, the sub-wavelength structures of metasurfaces are virtually dissipation
free (even near polaritonic resonances), if a transparent dielectric is used as the lens
material. Lack of material dissipation and reduced reflectivity avoids the problem of
insertion loss for these meta-lenses.
Similar dielectric diffractive structures have been used for designing physically thin
versions of various optical components, including blazed gratings [162–165], waveguide
couplers [166–168], and computer generated holograms [169,170]. Flat lenses based on
diffractive structures have also been proposed [165,171,172] and demonstrated [171].
For example, a TiO2 blazed grating lens has been developed for a wavelength of 860
80
nm, with a demonstrated focal length of 400 μm [164,173]. Other similar lenses were
proposed for on-axis and off-axis imaging [161, 164, 174]. A similar lens operating in
the visible range (650nm) has been proposed using silicon pillars on an oxide substrate.
Although silicon is absorbing in the visible and NIR range, losses in the proposed
lens are on the order of 20% at an operational wavelength of 650nm when using a
transparent substrate, due to the small volume fraction of Si in the structure [175].
Hence, the phase mask depth variation Δφ ≈ 2πδnh/λ0 ∼ 2δn · rad < 2π
8.2 Approach
We have developed a simple design for a thin dielectric meta-surface lens that
can be easily manufactured with relaxed tolerance, compared to precision diffractive
structures. The objective was to create a sub-wavelength, fine-patterned meta-surface
as a phase mask with a smooth radial dependence of phase increment on transmission,
avoiding 2π phase steps. Quasi-parabolic radial gradients of phase along the surface
were created by slow variation of geometric parameters of the fine pattern. The
meta-surface thickness is approximately one-third of the free-space wavelength (λ =
1.55μm, and height ≈ 0.5μm), in our specific case. Hence, the phase mask depth
variation, Δφ ≈ 2πδn(h/λ0) ∼ 2 ·δn ·rad < 2π across the lens area is relatively small.
Therefore, the mask covers just one single central Fresnel zone of the transmitted
beam, rather than multiple Fresnel zone rings with 2 phase steps as are typical in
a diffractive lens structure. As our experiments show, a mask of this type can be
sufficient to reduce a laser spot diameter by a factor of about three, which can be
very useful for many laser receiver applications.
For a proof-of-concept demonstration, we selected a nano-patterned regular array
of pillars etched with near vertical walls over the silicon wafer surface. The periodicity
of pillar positions has been chosen to be constant over the entire lens, while the
pillar diameter gradually varies from the lens center to its periphery to create spatial
variations in effective refractive index of the meta-layer. To obtain a phase mask with
81
only 0th order diffraction that minimizes scattering loss into other diffraction orders
of the periodic structure, the periodicity of the pillar structures must be less than
the structure cutoff scale, λ0/n, where λ0 is the wavelength in free space, and n is
the refractive index of the substrate. For the case of 1.55μm incident light with a
silicon substrate, the pillar periodicity should be less than about 445nm (here, 440nm
was chosen). The pillars were arranged into a square symmetry lattice in the x-
and y- (in-plane) directions to guarantee polarization isotropy and the same optical
characteristics under both x- and y-polarization. As a first approximation, we assume
that all pillars will have approximately the same height (given by the etching depth)
due to the simultaneous etching of all structures.
Before fabrication, a commercial software package utilizing Finite Element Method
(FEM) was used to simulate the optical properties of various structures. A paramet-
ric three-dimensional model of periodical pillar structures was simulated, and phase
increments of transmission and reflection were calculated. Parametric sweeps were
run over the pillar height, diameter, and wall slope to find structures exhibiting both
low reflection and large phase increments. Due to practical fabrication reasons, all of
the pillar heights and wall slopes were maintained constant across the entire structure
in simulations, while the pillars diameter were varied across the surface providing
the required phase distribution.
The phase of a wavefront incident on a conventional lens is modulated by the lens
curved profile resulting in lateral variations of the optical path due to glass thickness
variations across the lens. Similarly, a dielectric meta-lens alters the optical path
length (phase) of the transmitted light. The lens thickness is constant, and it is
the effective index of the layer that varies, as takes place for conventional gradient
index (GRIN) lenses. Using pillars of different diameters while maintaining the same
periodicity, the volumetric fill factor of the substrate material (vs. air) can be tailored
across the metalayer surface. Extended dynamic range of the phase variations in the
transmitted light requires a large variation in the effective refractive index of the
sub-wavelength thin modified layer. The dielectric metamaterial forming the desired
82
meta-layer provides this capability. A plane wave incident on this lens will exit the
surface with the curved phase profile characteristic of a positive focusing lens are
shown in Fig. 8.1
Fig. 8.1. Plane wave-fronts (shown in red) travelling through a con-ventional thick, curved lens (a), compared to a thick gradient index(GRIN) lens (b), and to a thin, flat meta-surface lens (c).
8.3 Design
Pillars with a small diameter will result in a low fill factor, mostly dominated by
the air between the pillars; and the effective index will approach that of air, index
n = 1.0. Such areas of the pattern will accumulate a small leading phase, and are
placed at the periphery of the lens. Thicker pillars with larger diameters result in a
higher volumetric fill factor with a higher attendant effective index; and these will
accumulate a large lagging phase, slowing the wave-front of the incident field.
Our models show that the effective index of actual meta-layer-induced deviates
from the simple direct proportionality to volumetric filling factor. As an example, in-
teractions of transmitted light with localized polaritons in the nano-structures results
in pushing more light into volumes occupied by the high index substrate dielectric.
In general, dielectric meta-layers can be designed to provide sharper spatial phase
gradients than ones anticipated from simplified fill-factor effective medium model.
Fabri-Perrot type of spectral resonances created by incident light multi-bouncing be-
tween two interfaces bordering the meta-layer one at the air side, another at the
83
substrate side should also be accounted for. In particular, transmission and reflec-
tion characteristics of the metalayer become dependent on wavelength and on angle
of incidence.
The lenses examined in this paper are each 30μm × 30μm in size, and square-
shaped. The nano-pattern for every lens consists of five concentric “belts. The belts
are formed by a discrete collection of square tiles, each 3μm x 3μm in size. The pillars
diameter is constant over the whole surface for every tile, see Fig. 8.2. Thus, the belts
were formed by pillars with constant diameter. We explored two designs square and
rounded lenses, both shown on the images in Fig. 8.2. The diameter of the pillars
changes from belt to belt (see Fig. 8.4), and belts are arranged with thick pillars near
the lens center and thin pillars towards the periphery.
Fig. 8.2. Top-view of the two realizations of the lens designs: a squarelens (left), and the rounded lens (right), with notched belt corners.The colored region shows the arrangement of the belts for each lens.
8.4 Fabrication Method
The pillar structures were fabricated by first patterning the circular discs used
as a mask for dry etching, (Fig. 8.3). The lithography was done using a Leica VB6
electron beam writer on a double-side-polished silicon substrate with ZEP resist.
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Upon lithography and development, a 45nm thick aluminum mask was deposited,
preceded by a 2nm titanium adhesion layer via electron beam evaporation. The ZEP
resist was removed via lift-off, leaving the aluminum mask on the substrate - used
for etching. The etching was performed over the entire substrate, leaving behind
only the small areas protected by the aluminum mask. Upon plasma etching, these
aluminum circular discs leave behind cylindrical silicon pillars rising up from the
flat, etched substrate. Three alternating steps of Reactive Ion Etching (RIE) and
Scanning Electron Microscopy (SEM) were performed. In each step, the etching
recipe was altered to ensure vertically etched sidewalls, and precise etching depths.
After reaching a depth of 550nm, the aluminum mask was removed using Nanostrip,
leaving behind the array of vertical silicon pillars of different diameters.
Fig. 8.3. Schematic showing the major steps of the fabrication process.
In total, three different combinations of five nano-patterns for every lens were
selected to provide gradual variation of transmitted phase increments using prelimi-
nary modeling predictions. Altogether, 15 different nano-patterns for tiles were used
to design all the lenses. SEM photos for two of the 15 of nano-patterns are shown in
Fig. 8.4. For every combination of the belt patterns, both square and rounded lens
tile geometries (see Fig. 8.2) were applied to design 30μm x 30μm lenses. Moreover,
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to reduce the risk of manufacturing accuracy, every lens design was implemented in
three versions: one was patterned with an optimal pillar diameter, while another two
had small deviations from the optimum, both larger and smaller values. So, in total,
18 different lens realizations were patterned and fabricated on the same wafer.
Fig. 8.4. Side-view of the pillar structures that modulate the phaseof light passing through the lens. Pillars of large and small diameteretched to similar depths.
Along with the lenses, 15 (120μm x 120μm) arrays of pillars were fabricated
simultaneously on the same wafer. These 15 arrays were patterned uniformly, each
containing pillars with the same diameter over the entire area. These replicate the
nano-patterns for all 15 elementary tiles we used for the lens designs. The additional
arrays allowed independent measurements of transmission through such patterns,
which were required to validate the model.
8.5 Phase Increment Measurement
Upon fabrication, SEM images of the 15 large (120μm x 120μm) arrays were mon-
itored to measure the final dimensions of the pillars in each array. These parameters
were fed into the original 3D FEM model, simulating predictions for the reflection and
phase of the field passing through each uniformly patterned tile. To experimentally
validate our model, the phase acquired upon crossing the pillar arrays was experimen-
tally measured using the shearing interferometer technique setup shown in Fig. 8.5.
The incident beam spot straddled the interface between the patterned region and the
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bare silicon surface, so that each half of the beam experienced different phase shifts
crossing the wafer. The position of the interference fringes (formed by interfering
these two parts of the illuminating laser beam) were compared to fringe positions
when the sample was laterally shifted so that both parts of the beam crossed the
un-patterned area of the wafer. As a result, a phase increment accumulated upon
passing through each pillar array was compared to the increment accumulated upon
passing through the surrounding flat substrate of the same thickness.
Fig. 8.5. Experimental setup for optical phase measurements. Thephase of each uniform array was measured by detecting the lateralshift in the interference pattern created between the beam passingthrough the patterned surface and the bare silicon surface.
The experimentally measured phase shift of each uniform array is shown and com-
pared to the computer simulations in Fig. 8.6. We clearly see a close correspondence
between the simulated and measured phase, and the simulations are well within the
margin of experimental error.
The arrays in the set we tested were enumerated using the following convention.
Of these 15 structures, arrays 1-5 were used to form the 5 sequential concentric belts,
starting from the lens center. Patterns 1-5 were used for lens design #1. Arrays 6-10,
similarly, refer to the concentric belts of lens design #2. Finally, the arrays 11-15 form
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Fig. 8.6. Simulation (blue) and experimental measurements (red) forphase increments added by patterned meta-surfaces for the 15 pillarstructures. The black error bars represent the 15% margin of error inthe experimental measurements.
the concentric rings of the lens #3 design. Collectively, the gradual phase variations
from belt to belt of the lens will shape the wavefront, producing the focusing behavior
of the lens (as sketched in Fig. 8.1).
8.6 Focusing Effect
Focusing properties of the meta-lenses were experimentally studied in a separate
set of experiments. The surface of the silicon wafer lens was illuminated from the
patterned side with a collimated 1.55μm laser beam, shown in Fig. 8.7. The goal
for this experiment was to monitor the spatial structure of the beam spot after the
light had been transmitted through the lens. Different beam cross sections were
imaged behind the lens with a high magnification onto an InGaAs camera (with a
magnification factor of about 1:30). The evolution of the diffraction pattern (which is
induced by the nano-patterned phase mask) was captured by displacing the position
of the imaging plane along the z-direction. A large diameter uniform beam (that
overfilled the lens), or a Gaussian beam approximately matching the size of the lenses
were used. The small diameter Gaussian beam was deliberately tilted at a small
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angle (about 10◦), with respect to the normal. This tilt helped avoid interference of
the transmitted light with secondary reflections from the 0.5mm thick silicon wafer
surfaces that could potentially interfere with the primary images. A microscope
objective placed directly behind the silicon wafer collected light and used for imaging.
The position of the imaged cross-sections was varied in small increments by displacing
the microscope objective position, or by moving the camera along the z-direction.
Fig. 8.7. Schematic of the focusing effect demonstration. The singlemode radiation from an Er fiber laser was tightly focused on the Sisample surface to monitor beam diffraction behind the surface micro-lens using a simple imaging system.
Fig. 8.8 illustrates the dynamics of the focal spot evolution along the z-axis behind
one of the micro-lenses. Here, the wafer was illuminated by a large beam at normal
incidence. The spatial fluctuations seen in the background of the figure are artifacts
typical in coherent imaging. Imaging the wafer surface plane where the lens is located
(z = 0) provides a reasonably flat intensity profile. At a distance of about 160μm
behind the micro-lens (inside the wafer), the light is focused to a round spot of highest
concentration. This spot is much smaller than the 30μm x 30μm size of the micro-lens
(which is depicted as a yellow box in Fig. 8.8). The positions of the image plane have
been calculated to account for refraction of the imaging light at the output Si/air
interface. When shifting the image plane further into the wafer bulk, the spot size
increases. The beam spreading continues more rapidly when light escapes from the
Si wafer into air.
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Fig. 8.9 shows the intensity distribution at different imaging planes for the case
when a 24μm diameter tilted Gaussian beam illuminated the square micro-lens (left
photo in Fig. 8.2). Right at the micro-lens location (i.e. at input interface of the
wafer) plane, the original Gaussian profile is seen. The plane of minimal spot size
(which we call the focusing plane) is shown in the middle, along with the plane one
focal length behind the focusing plane, shown on the right. The plot in Fig. 8.9
compares the original Gaussian intensity profile with the profile at the focal spot. It
can be seen that the lens reduces the beam spot size by nearly a factor of three - the
FWHM of the incident light is decreased from 32μm to 11μm. The on-axis intensity
increases by a factor of 1.87 in this case (compared to input beam intensity).
Fig. 8.8. Intensity profiles taken at different image planes behindthe micro-lens surface measured from the input surface of the wafer.The micro-lens is strong enough to focus light inside the wafer. Theyellow-color frame depicts a 30μm x 30μm box equivalent to the sizeof the micro-lens.
The photos in Fig. 8.9 demonstrate that along with the tightly focused spots, a
halo pattern around the spots is present near the focus. The light power distributed
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Table 8.1Lens Characteristics
Bare Si Wafer Circular Design Square Design
Front Surface Reflectivity 30% 11% 14%
Portion of Input Power in
15μm× 15μm spot
17.5% 35% 35%
Distance (μm) to the po-
sition with maximal con-
centration in 15μm× 15μm
spot
N/A 450 510
Focal distance defined by a
minimal spot size
N/A 122 221
over the halo around the spots explains why the peak intensity increase at the focal
spot center is less than would be expected from just beam area reduction. The
halo carries imprints of the square symmetry of the lens design, which indicates that
the halo is an aberration effect associated with the discrete tiled square lens design.
Another plausible explanation is insufficient amplitude of the phase mask for this first
realization of the micro-lens design. Perfecting the lens design, making the phase mask
deeper and the step size more gradual could increase the light intensity at the tight
focal spot, as compared to intensity of the incident light, by an order of magnitude.
Table 1 shows examples of the optical characteristics for two different micro-
lenses, along with a comparison to a bare, flat silicon wafer (with unmodified surface).
First, the surface reflection is reduced from 30% for a planar silicon surface to only
11% or 14% for the nano-patterned surfaces (due to improved impedance matching).
Second, lens focusing power for this microlens should be characterized by two different
parameters: distance to a plane of minimal spot size, and a distance to a plane
with maximal power concentration within a smaller square, (such as a quarter of the
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original square lens area). In particular, more than one-third of the input beam power
can be concentrated into a half-pixel size square, 15μm x 15μm, near the center of
a beam passing through the lens. Meanwhile, peak intensity can be doubled (Fig.
8.9) at the plane of smallest spot size when compared to the flat silicon wafer. Focal
distances observed for our 18 micro-lenses varied from about 160μm (see Fig. 8.8),
up to approximately half a millimeter, 450μm and 510μm for the two lenses with
a circular and square design, respectively (as listed in Table 8.1). This variation
is due to both the variety of lens designs tested, as well as to finite tolerance of
manufacturing process used.
Fig. 8.9. The light intensity distribution at the micro-lens surface (a),at the minimal spot size focusing plane (b), and at two focal lengthsbehind the focusing plane (c). The yellow frame depicts a 30μm ×30μm square representing the size of the original lens. Secondaryreflection spots are visible near left lower corner of the photos. Theintensity of the Gaussian beam at the micro-lens input (green) iscompared to the measured intensity at the focusing plane (blue) forone of the micro-lenses (d). This particular micro-lens increased theaxial intensity by a factor of 1.87.
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8.7 Conclusion
In conclusion, we have demonstrated a sub-wavelength thin planar all-dielectric
metamaterial lens patterned on a silicon wafer surface. A transparent dielectric sub-
strate with no metal elements avoids light absorption as light passes through the meta-
material layer (in contrast to plasmonic meta-surfaces). One key advantage of this
micro-lens design is a reduction in the insertion loss for wafer-level integrated micro-
lenses down to about 10%, making this approach suitable for a variety of narrow-band
and moderate bandwidth transmitting lens applications. Although the focusing sur-
face layer was only about 0.5 μm thin, the resulting lens demonstrated a focusing
distance of less than 0.5 mm with an attendant reduction in spot size by a factor
of three. To design such lenses, we have created a parametric computer model that
can calculate the phase of a plane wave passing through pillar structures of varying
geometric parameters (including height, slope and diameter). These computer sim-
ulations show close correspondence with experimental measurements on fabricated
structures.
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9. STUDIES OF METAL/DIELECTRIC COMPOSITE
SUPERLENS
9.1 Motivation
There is a great deal of interest to utilize an enhanced near-field EM signal. How-
ever, as close proximity to a metal surface can provide adverse effects to the sample
in question, there is strong interest in creating this strong evanescent enhancement
away from the metal surface. For this reason, we have studied the ability of a lamellar
near-field superlens to transfer an enhanced electromagnetic field to the far side of
the lens. In this work, we have experimentally and numerically investigated super-
lensing in the visible range. By using the resonant hot-spot field enhancements from
optical nanoantennas as sources, we investigated the translation of these sources to
the far side of a layered silver-silica superlens operating in the canalization regime.
Using near-field scanning optical microscopy (NSOM), we have observed evidence of
superlens-enabled enhanced-field translation at a wavelength of about 680 nm. Specif-
ically, we discuss our recent experimental and simulation results on the translation of
hot spots using a silver- silica layered superlens design. We compare the experimental
results with our numerical simulations and discuss the perspectives and limitations of
our approach. In this scheme, the localized and enhanced electromagnetic fields (or
hot spots) could be created by optical nanoantennas [15, 18, 176, 177], and the hot-
spot transfer with a superlens could be useful in applications such as surface-enhanced
Raman spectroscopy (SERS) [178] or enhanced fluorescence microscopy [23]. Optical
hot spots are important for a range of important bio-, chemical- and medical-sensing
applications, including surface-enhanced Raman scattering [179] and enhanced flu-
orescence [177]. It has also been shown theoretically that an optical hot spot can
be translated through a near-field superlens [180]. Such a setup is preferable to di-
94
rect contact with a metal, which has been shown to cause structural and functional
changes in biomolecules [181], including denaturation of proteins [182]. Furthermore,
very close proximity with metal nanoparticles can cause fluorescence to be quenched
rather than enhanced [183].
9.2 Background
In 1873, Ernst Abbe postulated that it is impossible to focus light below a certain
limit due to diffraction effects. Termed the Abbe limit or the diffraction limit, this
idea was fundamentally challenged in 2000 with the proposal of a sub-diffraction su-
perlens by Pendry [7], which was based on the 1968 paper on negative-index materials
by Veselago [6]. Pendrys initial superlens would, in principle, work for propagating
(or far-field) waves and would allow unlimited resolution in the image of an object.
This superlens design required some rather strict conditions on the permittivity and
permeability of the superlens material, however. Pendrys proposal also included
a simplified, near-field superlens design that required only a negative permittivity,
rather than simultaneously negative permittivity and permeability. Near-field super-
lensing was experimentally demonstrated in 2005 by Fang and coworkers [26] and
nearly simultaneously by Melville and Blaikie [27], followed by others [184]. However,
the practical applications of near-field superlenses are still quite limited due to the
fact that the permittivities of the lens and the surrounding medium must be equal in
sign and opposite in magnitude. Because many metals have negative permittivities
in the visible range, they are a natural choice for superlenses. For superlensing opera-
tion, the matching condition εmetal = −εdielectric must be satisfied [7] for the real parts
of the permittivities. For dispersive materials, this condition means that superlens
operation can only be achieved at a single wavelength for each material system. In
the case of the silver-polymer combination used in many of the initial near-field su-
perlens demonstrations, the matching condition is met at a wavelength of around 365
nm [6,26,27]. However, superlensing in the visible or near-infrared wavelength range
95
promises a number of exciting applications. Several solutions have been proposed to
bring superlensing to this spectral range, including the use of metaldielectric compos-
ites (MDCs) [28, 185–187] and multilayer lens structures. These solutions allow the
designer to select or tune the superlens operational wavelength by adjusting the fab-
rication procedure appropriately. Note that in using the term tune here we mean that
the operational wavelength of the superlens can be selected prior to fabrication. If
such a tunable near-field superlens could be achieved, it would open up many promis-
ing applications based on the spatial translation (or transfer) of highly localized,
enhanced electromagnetic fields [188–195] to the other side of a superlens [196].
Although we have studied both MDCs and multilayer superlens designs in our
research, here we focus on the latter category, specifically lamellar, multilayer metal-
dielectric devices for superlensing in the visible range. Therefore, as a side note, we
briefly mention some of the experimental [197] and numerical simulation [198] results
on our work with MDC films. Metal-dielectric composites or MDCs are materials
that consist of a random mixture of subwavelength metallic in a dielectric host (or al-
ternatively, small dielectric particles in a metallic host); such materials are sometimes
called cermets. In principle, according to effective-medium theories, MDCs permit
a designer to adjust the effective permittivity of the mixture through selecting the
constituent materials and the relative volume fractions. Ideally, such a MDC material
should produce a selectable effective permittivity at any wavelength in a wide range
while maintaining low loss. We have observed that it is indeed possible to adjust the
real part of the permittivity of a superlens based on MDC films, and hence the su-
perlens operational wavelength can be tailored for a particular application simply by
altering the volume ratio between the metal and dielectric components in the compos-
ite. However, we also discovered that passive MDC designs are inherently too lossy
to be useful in real superlens applications [197, 198]. It is due to this overwhelming
loss that we turned our attention to lamellar, multilayer superlens designs.
Single-layer and multilayer near-field superlenses have been studied by a number
of researchers in recent years. Most experimental studies have focused on the plas-
96
monic operational regime, which is limited to the near-UV range for noble metals and
common dielectrics. In this regime, the matching condition is met directly through
the careful selection of the metal and dielectric materials, and the wavelength of op-
eration is not adjustable once the material combination is determined. Numerical
studies have also predicted the existence of a canalization regime in which superlens-
ing occurs in a highly anisotropic, layered, metal- dielectric system at wavelengths
away from the plasmon resonance and into the visible range. This canalization regime
has been experimentally observed in the microwave range. In this work, we have ex-
perimentally and numerically investigated superlensing in the visible range. Using
the resonant hot-spot enhancements from arrays of optical nanoantennas as sources,
we investigated the translation of these sources to the far side of a layered silver-silica
superlens operating in the canalization regime. With the technique of near-field scan-
ning optical microscopy (NSOM), we have observed evidence of superlens-enabled
enhanced-field translation at a wavelength of about 680 nm. The experimental evalu-
ation of the fabricated samples included NSOM, scanning electron microscopy (SEM),
atomic force microscopy (AFM) and far-field spectroscopy. We have also studied the
samples extensively using FDTD simulations to evaluate their near-field electromag-
netic behavior. Finally, we summarize and compare our experimental results with
respective numerical simulations and discuss the perspectives and limitations of our
approach.
Lamellar, multilayered metal-dielectric systems such can be used for wavelength-
selectable near-field superlenses in the canalization regime. A schematic of such a
multilayered lens design is shown in the left panel of Figure 9.1, and an SEM image
of a prototype multilayer structure is shown in the right panel of the figure. These
multilayered metal-dielectric systems can be considered to be uniaxial crystals that
exhibit a flat, hyperbolic dispersion relation [33,179]. Multilayered systems have been
extensively studied theoretically, and their lensing and optical properties have been
discussed by a number of authors [148, 179,180,199,200].
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Fig. 9.1. Schematic of a lamellar, alternating multilayer metal-dielectric system (left). The metal is white, the dielectric is gray,and the layers are subwavelength in thickness. This scheme providesa method of adjusting the operational wavelength of a superlens. Across-section SEM view of a silver- silica prototype superlens designwith layer thicknesses labeled (right).
A metal-dielectric multilayered system with subwavelength layer thicknesses ex-
hibits an anisotropic permittivity characterized by the dispersion functions (9.1) [179]
εx = εy =εdd1 + εmd2d1 + d2
, εz =
(ε−1d d1 + ε−1
m d2d1 + d2
)−1
(9.1)
where εd and εm are the bulk permittivities of the dielectric and metal constituents,
respectively, and the thicknesses are as labeled in Fig. 9.1. In superlensing applica-
tions, we are interested in obtaining a system with a parallel permittivity of unity
for impedance matching (εx = εy = 1) and an infinite perpendicular permittivity
(εz → ∞). This is known as the canalization regime [179]. In practice, however,
due to losses and material limitations, both conditions cannot be fulfilled simultane-
ously. These multilayer films are not restricted to operation at a single wavelength
for a given material combination; the operational wavelength can be tuned simply by
altering the relative thicknesses of the metal and dielectric layers.
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9.2.1 Nanoantenna Pattern Design and Fabrication
As stated above, we were primarily interested in studying the ability of a near-
field superlens to transfer field-enhanced optical hot spots, and hence our first step
was to design an array of optical nanoantennas to produce these hot-spot sources.
The antenna design was based on pairs of identical rhombus-shaped metal structures
with a narrow gap between the two. It is in this narrow gap where electromagnetic
energy is localized and where the hot spot is produced. These very high local field
intensities are created between antenna pairs only when the pair is illuminated with
correctly polarized light (that is, light that is polarized parallel to the long axis of the
antenna pair). This antenna design choice was selected based on existing expertise
from previous work [177].
Schematic designs of our antenna array are shown in Fig. 9.2. Each individual
antenna has a characteristic size X, which is the length of the minor axis. In our case,
X was about 80nm. The major axis is twice as long (160nm), and the second antenna
is placed along this axis, with a gap of 20nm separating the two. The antenna pairs
are spaced with a periodicity of 4X (320nm) along the minor axis and 8X (640nm)
along the major axis (see Figure 9.2).
The nanoantenna fabrication was performed by electron-beam lithography (EBL)
on a quartz substrate in large, 500μm × 500 μm arrays in order to permit far-field
optical characterization the final samples. Following EBL photoresist patterning and
development, a reactive-ion etch procedure was used to create 40nm holes in the
quartz substrate. Next, a 1nm layer of Ge followed by a 40nm layer of Ag was
deposited into these holes, resulting in a flatter topography than would be possible
without etching. For simplicity, light polarized along the major axis (across the gap)
will be referred to as parallel or x-polarized, while light polarized along the minor
axis will be referred to as perpendicular or y-polarized light. The antenna array
was designed to be resonant under parallel-polarized light at a wavelength of about
633nm.
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Fig. 9.2. Schematics of the basic nanoantenna design. (a) A nanoan-tenna pair in top view and cross section. Two 40nm thick rhombus-shaped antennas form a single pair and are spaced 20nm apart. Theantenna pair is embedded into a quartz substrate. (b) The individualantenna pairs are part of larger arrays. The size of the individualantennas is related to the spacing of the array. The size parameter Xcan be varied in order to achieve different resonance wavelengths. Inthe arrays we studied in this work, X was 80nm.
9.2.2 Superlens Design
The superlens design was based on finite-element model (FEM, COMSOL Multi-
physics) calculations and modeling using a chromium grating to simulate lens perfor-
mance at a resolution of 100nm, which was the grating half-pitch. The results from
these initial numerical simulations indicated that subwavelength resolution might be
possible without impedance matching, with λ/6 resolution achieved for a single-layer
silver lens with a SiO2 host. The highest contrast was achieved for a three-layer
superlens design. However, the intensity transmission through the sample was ex-
pected to be too low for NSOM measurements for this configuration. As a result, a
single-layer design was chosen since it provided the best compromise between contrast
100
and transmission. The superlens design consisted of a 20nm silver layer covered on
both sides by 21nm SiO2 layers. While not included in the model, a 1nm germanium
adhesion layer was added below the silver layer in order to lower the silver roughness
and decrease the loss. The germanium layer itself is not expected to add much loss
due to the very low thickness and relatively low loss at 633nm.
We designed and fabricated three different types of samples for our experimental
investigations. Although the three sets of samples have exactly the same nanoantenna
design, the regions above samples differ in their overlayer designs (see Figure 3). The
first sample type was simply uncovered or bare nanoantennas with no overlayer. In
the superlens samples, the nanoantennas are covered with 21nm of silica, 20nm of
silver, and another 21nm of silica. In the final type of sample, the nanoantennas
were covered with a 62nm silica layer. This is an equivalent thickness to that in
the superlens samples, and hence these samples were used as reference samples. The
reference and bare nanoantenna samples were used to compare the near-field intensity
distributions to those of the superlens samples. In all samples, the overlayers were
fabricated using electron-beam evaporation. The cross-sections of the three sample
types are shown schematically in Figure 9.3
9.2.3 Sample Characterization
We performed a number of tests in order to evaluate the quality of the fabricated
samples and to characterize their properties. These tests were focused on the antenna
shape as well as the planarization and quality of the silver layer. We first used
scanning electron microscope (SEM) imaging to study the uncoated antenna arrays,
an example of which can be seen in Fig. 9.4. The antenna shape was generally
well reproduced, though the finite size of metallic grains does lead to a rounding of
the edges. As we will show, this rounding was taken into account in our numerical
simulations. In general, however, the nanoantenna elements were all generally very
uniform with no missing antenna pairs.
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Fig. 9.3. Cross-section of the three types of samples examined inthis study. a) the bare antenna sample, b) the reference sample witha dielectric spacer above the antennas, and c) the superlens samplewith layered metal and dielectric films above the antenna arrays.
Fig. 9.4. SEM image of a nanoantenna array (X = 80nm). Thepattern is well reproduced with a gap size around 20nm. Some minorvariations in antenna shape can be observed, which can be ascribedto the finite metal grain size. The slight rounding of the corners ofthe nanoantennas is accounted for in our numerical simulations.
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We also used atomic force microscope (AFM) imaging to investigate the roughness
and surface quality of the embedded nanoantennas. Our goal was to produce a
flat final surface with minimized height deviations between the antennas and the
surrounding substrate within the antenna arrays. The AFM results (not shown here)
indicate that the embedding was generally very good, and the average height variation
between the antennas and the substrate was less than 5nm RMS. In addition, we
studied the quality of the deposited 35nm silver / 1nm germanium superlens layers
with AFM. This was done on a test sample with no SiO2 cover layer in order to allow
direct access to the silver material. The results show good film uniformity with a
small grain size and a low roughness of 0.5nm RMS. For comparison purposes, we
also deposited 35nm silver films directly on SiO2 with no germanium adhesion layer.
In this case, the AFM results show a much higher surface roughness of 2.7nm RMS.
9.2.4 Far-Field Characterization
The nanoantenna array was characterized optically via far-field transmission mea-
surements using a supercontinuum light source (Koheras) with a broad emission range
from 500nm to 2000nm. The light was focused on the sample with a focus size of 200-
300μm, and a linear polarizer was used to adjust the incident light polarization. After
passing through the sample, the light was refocused and coupled into a spectrometer.
Background reference measurements were taken through the sample in an area free
of visual defects and outside of the nanoantenna array. The reference intensities were
then subtracted from the array intensities in order to give a relative transmission
measurement.
As expected from theory [15,201], a strong resonance was seen for parallel-polarized
(x-polarized) light, and it is this resonance that is of interest in our work. For the
bare antenna array with a size parameter of X = 80nm, the resonance occurred at
a wavelength of 620nm, which is close to the expected 633nm resonant wavelength.
A weaker resonance was seen for light polarized orthogonal to the long axis of the
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antennas pairs (perpendicular or y polarization). This weaker resonance wavelength
was blue-shifted compared to that of the parallel polarization. Optical transmission
measurements were also performed after depositing the reference silica layer or the
silver/silica superlens layers on top of the bare antennas, and we observed significant
changes in the transmission spectra. For the reference sample, a red shift of about
40nm was observed in the resonance position. This shift was expected, since the SiO2
covering increases the refractive index around the antennas as compared to air. For
the superlens-covered sample, however, the red shift was slightly larger (45nm). In
fact, when we collected spectra from nanoantenna arrays with different size parame-
ters, we found that the resonant wavelength shift for silica-coated antennas was about
40nm for all arrays, while the shift for superlens-covered arrays depended on the ini-
tial resonance position. Antenna arrays with an initial resonance of about 500nm
showed no resonance shift with the addition of the superlens, while antennas with
a resonance around 700nm shifted by as much as 100nm when we added the super-
lens layers. We attribute this to coupling between the antennas and silver superlens
layer. As a result of this shift, the reference samples have a different resonance wave-
length than the superlens samples, even for otherwise identical antennas. Around our
wavelength of interest (≈ 633nm), the difference is slight, but for antennas outside
this range the difference can be significant, which complicates any direct comparisons
between the superlens and reference samples.
9.2.5 Near-Field Characterization
We performed a large number of NSOM scans in order to study the near-field
intensity distribution on the samples. These measurements were carried out at The
Max Planck Institute for the Science of Light and Friedrich-Alexander-Universitt
(Erlangen, Germany) and at Purdue University (West Lafayette, Indiana, USA).
The NSOM setup in Erlangen was equipped with an acousto-optic tunable filter in
combination with a supercontinuum light source, which enabled the selection of any
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incident-light wavelength from 450nm to 700nm. The setup also included a linear
polarizer, and NSOM measurements were taken with a highly modified Nanonics 4000
system. The NSOM setup at Purdue was a Nanonics 2000 system but was limited
to 633nm light and did not have polarization control in our measurements. In both
systems we used metal-coated aperture NSOM tips with sizes ranging from 150nm
down to 50nm, and in both systems we also used avalanche photodiodes (APDs) for
detecting the collected light intensity. Several types of NSOM scans are possible, with
each type providing different near-field information about the sample. Schematics of
three main NSOM modes are shown Fig. 9.5. In reflection-mode NSOM (Fig. 9.5,
left panel), the sample is illuminated in the near field via the tapered-fiber NSOM
tip, and the far-field reflected or scattered light is measured from the sample. In
transmission-mode NSOM (Fig. 9.5, middle panel), the sample is again illuminated
in the near field with the tapered-fiber tip, but in this case the transmitted light
is collected in the far-field. In our measurements we used collection mode NSOM
scanning (Fig. 9.5, right panel). In this case, the sample is illuminated from the
bottom with far-field light that is transmitted through the sample, and the near-field
intensity is collected with the NSOM tip.
Fig. 9.5. Three types of NSOM scanning modes. The thick arrowrepresents illumination of the sample. The thin arrows represent thecollected or measured light. In this work we focused on collectionmode NSOM (right panel) for our near-field measurements.
With the NSOM system in Erlangen, we performed numerous NSOM measure-
ments on the nanoantenna array with a size parameter X = 80 nm, and scans were
105
taken at wavelengths ranging from 530 nm to 680 nm in steps of 10 nm and with both
parallel and perpendicular light polarizations. At Purdue, measurements were done
at 633 nm with unpolarized light. In both systems, the measurements were done on
superlens samples as well as on reference samples and bare nanoantenna samples. The
scan sizes were either 5μm × 5μm or 10μm × 10 μm. The resolution was kept con-
stant at 128 data points per 5μm. We note that we have observed some complications
in interpreting our experimental NSOM results. These issues are related to several
factors, such as the fact that the fiber tips experience gradual degradation over time.
In addition, there are necessary manual alignments in both of our NSOM systems,
which is another source of discrepancies in comparing the data from one sample to
the next. When we combine these concerns with the automatic intensity rescaling
performed by the Nanonics software, we conclude that the measured intensity values
cannot be compared directly between scans.
9.3 Bare Antennas
When scanning the bare antenna samples under perpendicularly polarized (y-
polarized) light at 620nm, no resonance was observed, which is consistent with our
far-field measurements. In this polarization, the antennas simply block part of the
incoming light. Thus the antennas appear as regions with lower intensities, an exam-
ple of which is shown in Figure 9.6. The resolution in the scan in Fig. 9.6 is sufficient
to see individual antenna pairs, but we cannot resolve individual antenna elements.
When illuminating the array with light at the parallel polarization (x-polarized),
a periodic enhancement of the intensity is observed. This resonance has a periodicity
equal to the array periodicity, it overlaps with the light that is simply transmitted
through the sample, and its peak intensity is well above that of the incident light.
However, this is not the nanoantenna hot-spot resonance, which can be seen in two
ways. First, when we compared the AFM and NSOM data we observed that the
highest intensity regions are in the areas between the antenna pairs, whereas the hot-
106
Fig. 9.6. NSOM scan (left) and intensity cross-section (right) of abare antenna array illuminated with perpendicular-polarized light at620 nm. The antenna pairs can be observed as dark regions becausethey block some of the light transmitted through the substrate.
spot resonance should occur in the gap in the middle of the antenna pair. Second,
when looking at the edge of an array, we see that the periodic enhancement extends
well beyond the boundaries of the antenna array, as seen in Fig. 9.7. This behavior
shows that the resonance is actually a propagating mode, and thus it is not the
highly localized hot-spot nanoantenna resonance. Note in Fig. 9.7 and in many of
our NSOM scans that we were not able to reliably resolve the antenna pairs in the
vertical direction of the image (the y-direction) because the periodicity is smaller in
that direction.
At this point it is important that we note some peculiarities of our antenna ar-
ray pattern with respect to the expected resonance wavelength of the reference and
superlens samples. It has been shown that coupled nanoantenna resonances die out
when the distance between the antenna elements exceeds 2.5 times that of the parti-
cle size [201], which is why the nanoantenna arrays used here have a spacing of three
times the particle size (corresponding to center-to-center distance of four times the
size parameter X, or about 320 nm for our X = 80nm array). However, for our silver
nanoantennas this spacing had the unintended consequence of producing a period-
icity (8 × 80nm = 640 nm) that is very close to the shifted resonance wavelength
of the reference and superlens samples. As a result, the nanoantenna array acts es-
107
Fig. 9.7. NSOM scan (left) and cross-section (right) of a bare nanoan-tenna array illuminated with parallel-polarized light at 620 nm. Inthe cross-section scan, the antenna array boundary is at 4 μm. A pe-riodic resonance is observed that extends well beyond the boundariesof the array and decays with distance from the array. In this resonantmode, the peak intensities are significantly higher than that of theincident light.
sentially as a grating with a periodicity of λ in one direction and a periodicity of
λ/2 in the other direction; such gratings have been shown previously to couple light
from free space into propagating surface or waveguide modes [202, 203]. We expect
this grating-coupled propagating mode to travel inside the silica of the substrate it-
self, which could act as a waveguide due to its high refractive index compared to the
surrounding air. We will discuss this grating-coupled mode in more detail in later
sections.
9.4 Superlens and Reference Samples
Returning to our preliminary NSOM data, we observed a different field-enhancement
distribution near the expected resonance wavelength of 665nm (620nm + 45nm shift)
on the superlens samples. Here a second resonance appears with the same spacing
as the periodic mode described earlier but shifted by half a period. As shown in Fig.
9.8, this resonance is not present at 620nm, but it can be seen as very low intensity
peaks at 650nm, and it is even stronger still at 680nm. At 680nm this extra resonance
108
mode reaches roughly the same intensity as the propagating mode, which gives it the
appearance of a simple doubling in frequency. No scans were performed at longer
wavelengths, since the wavelength limit of the setup had been reached, so it is not
known if the intensity grows even more at longer wavelengths.
Fig. 9.8. NSOM scans of the intensity distribution (left) and intensitycross-section (right) measured on a superlens sample for three differentwavelengths. At 620nm (top) only the propagating mode is seen, at650nm (middle) a weaker second mode starts to appear, and at 680nm (bottom) the weaker mode has grown in strength to equal thepropagating mode.
109
In addition to the appearance of this second resonance, we also see that the widths
of the intensity peaks were reduced significantly at 680nm. In order to investigate
the origin of this second resonance, an NSOM scan was performed using the same
wavelength (680nm) but with perpendicularly polarized light, and the results show
no sign of the additional resonance. Furthermore, identical scans were taken on a
reference sample to see if this effect was related to the silver superlens layer, and once
again no secondary resonance was observed. These scans are shown in Fig. 9.9
With this preliminary NSOM data in mind, we conclude that there were two main
phenomena occurring in our results. The first and most interesting was the appear-
ance of the second resonance mode, which occurred only near a specific wavelength
and in a particular polarization. The second phenomenon was the narrowing of the
intensity peaks. We see three possible contributions to the near-field intensity pat-
terns in our NSOM scans: (1) light transmitted through the sample in the bare areas
between the antenna pairs, (2) the grating-coupled propagating mode, and (3) the
localized field enhancement from the nanoantennas. Because the secondary resonance
appears very close to the expected resonance frequency of the nanoantennas, and only
at the correct polarization, it appears to be our sought-after nanoantenna hot-spot
resonance.
Furthermore, the narrowing of the intensity peaks would be consistent with an
increased extinction cross-section for the nanoantennas at resonance, which would
have the effect of stealing light from the surrounding area. This line of reasoning
suggests that this additional field enhancement is indeed the localized nanoantenna
resonance, and that the superlens allows it to be resolved on the far side of the lens,
which is not possible on the reference sample. However, due to the similarity of this
resonance to the propagating mode, more information and additional measurements
are needed to confirm this hypothesis. In the next section we discuss these further
measurements as well as the numerical simulations we performed in support of our
experimental results.
110
Fig. 9.9. Comparison of the NSOM intensity distributions for thesame antenna array under three different conditions. In addition tothe propagating mode, a second resonance mode was observed for theparallel polarization on a superlens sample (top panel), which causedthe appearance of frequency doubling. No such mode was observedfor the perpendicular polarization on the same sample (middle), orfor the parallel polarization on a reference sample (bottom). All datawas taken at an incident wavelength of 680 nm.
9.5 FDTD Simulations for Far-Field Spectra and Near-field Intensity
Maps of the Superlens and Reference Samples
After obtaining our preliminary NSOM results, it was clear that numerical simu-
lations on the antenna structures and cover layers would give us valuable insight into
111
understanding the intensity profiles in our experimental results. We chose to use the
finite-difference time-domain (FDTD) method for our simulations because the results
with our new generalized dispersion model [204] are quite accurate and, with the
extensive cluster computing facilities available at Purdue, full 3D simulations were
possible.
As noted previously, the fabricated nanoantennas were slightly more elliptical
than the initial rhombus-shaped design. Because the shape of the antenna plays a
strong role in determining the overall plasmonic response, more realistic elliptical-
shaped antennas were used in our simulations. The gap between antennas was fixed
at 20nm, and the geometry of the simulated unit cell of the antenna array can be
seen Fig. 9.10.
Fig. 9.10. Elliptically-shaped nanoantenna pair used as the unit cellof the array in the FDTD simulations. The shape of these antennascorresponds more closely with the actual shape of the nanoantennas,as indicated in our SEM results. In this image, white is metal (silver)and black is dielectric material (glass).
We calculated full-wave responses of the three types of samples at a variety of in-
cident wavelengths and polarizations. Some representative near-field intensity maps
are shown below. In the simulated intensity maps, many unit cells are shown in an
array in order to mimic the scan area of the experimental NSOM results. The inten-
sities were calculated at a distance of 10nm above the top surface of the sample; this
was done in order to mimic the NSOM tip scanning distance. Finally, the calculated
112
intensities were averaged with a 150nm circular averaging function in order to mimic
the aperture area of the NSOM tip. For convenience, the ellipses in the lower left area
of each image show the locations of the nanoantennas inside the simulated domain.
The details of the material models used in our FDTD simulations can be found in
our previous publication [198].
The nanoantenna structures were simulated for the three sample types (bare an-
tenna, superlens, and reference sample) using fully 3D FDTD calculations. The bare
antenna sample was simulated under 620nm and 633nm illumination schemes, corre-
sponding to the resonance wavelength and the Purdue NSOM laser source, respec-
tively. The superlens and reference samples were each simulated at 660nm and 680nm,
corresponding to the measured far-field resonance and the wavelength of the observed
double-periodicity pattern, respectively. For each wavelength, the field distributions
were calculated under parallel polarization (x-polarized, resonant case) as well as un-
der perpendicular polarization (y-polarized, off-resonant case). For each polarization,
the field intensity components were calculated along each axis direction (|Ex|2, |Ey|2,|Ez|2). The computational domain used for these simulations was 640nm and 320nm
in the x- and y- directions (the z- direction is normal to the substrate surface), and
was 4000nm in the z- direction. The spatial discretization was 5nm, and the time
discretization was about 4.814583×10−18s. We used perfectly-matched layer (PML)
boundaries in the z- direction, and periodic boundary conditions (PBCs) were applied
to all other sides (that is, in the x- and y- directions) of the simulation domain. The
electric field (E-field) and magnetic field (H-field) for each unit cell were discretized,
and thus the intensity of each cell was defined as |Etotal|2 = |Ex|2+ |Ey|2+ |Ez|2. Thistotal field intensity (|Etotal|2) corresponds with the intensity measured experimentally
with NSOM. In all our FDTD simulations, the germanium layer was omitted and the
21nm and 62nm thicknesses were rounded-off to 20nm and 60nm, respectively. This
was done in order to accommodate the finite-sized grid of the simulation domain.
The incident wave illuminated the sample from the bottom in order to simulate the
experimental situation in collection-mode NSOM measurements.
113
9.5.1 Representative FDTD Near-Field Intensity Maps for Bare Antenna
Sample
In Fig. 9.11 we show representative FDTD near-field intensity maps resulting
from our numerical simulations. These intensity maps were calculated for the bare
antenna sample at an incident wavelength of 620nm for both polarizations. Since the
intensities are not normalized among the maps, corresponding scale bars are included
for each image. These maps indicate that in the parallel polarization the near-field
intensity is dominated by the x- and z-components of the field, while in the perpendic-
ular polarization it is the y component that dominates the total intensity. This trend
is consistent for all of our calculated intensity maps at all wavelengths. Notably, the
strong z-component contribution indicates a strong grating-coupled diffraction mode
within the intensity distribution. This corresponds to our earlier NSOM analysis
that there is a strong propagating mode in the antenna array under parallel-polarized
light.
9.6 Comparing FDTD Simulations to NSOM
We can now compare the total, FDTD-calculated intensity distributions |Etotal|2
to the experimentally measured NSOM results. For each sample (bare antennas,
superlens, and reference), we show images of the NSOM scans in the parallel and
perpendicular incident light polarizations. The FDTD simulation results for the same
polarizations are shown below the corresponding experimental scans. Schematic insets
on the NSOM scans show the incident-light polarization and the orientation of the
antennas (not to scale). Although all the simulations results have been averaged
over an area roughly the size of the NSOM tip aperture, it is still obvious that the
simulation results are much clearer than the NSOM measurements. We attribute
this loss in resolution in the NSOM scans to a possible larger tip aperture due to
inevitable damage during scanning, to sample/tip interactions that perturb the near-
field, and/or to imperfections in fabrication. It should be noted that in most of the
114
NSOM measurements, the sample image is rotated roughly 15◦ from vertical. This
slight orientation offset is due to the fact that sample alignment in the NSOM is done
manually, and it is therefore quite difficult to align the sample precisely.
9.6.1 Bare Antenna Sample
We begin with our results for the bare antenna structure in Fig. 9.12. Both the
simulations and the NSOM results were performed with illumination at a wavelength
of 620nm, which corresponds to the transmission dip (resonance) observed in our
far-field measurements.
Note that, as before, we see stripes in the NSOM images due to the inability to
resolve the rows of antenna pairs, although we can resolve the columns of the array.
We see very little difference between the NSOM scans for the two polarizations on
the bare antenna sample (top row of Fig. 9.12). The only differences are slightly
broader high-intensity stripes in the perpendicular polarization than in the parallel
polarization. Comparing the FDTD results (bottom row of Fig. 9.12), we see that
the parallel-polarized light is strongly confined to the antenna gap, which is expected
from the previous far-field measurements, and the intensity does not extend as far in
the y direction as in the x-direction. In the case of perpendicularly polarized light,
the intensity is not localized to the antenna gap, and the intensity profile is broader
in both the x- and y-directions. Both of these results agree reasonably well with our
NSOM results.
9.6.2 Superlens Sample
In Fig. 9.13 we show the NSOM scans and simulation results for the superlens
sample measured and simulated with 680nm incident light. In this case, the FDTD
simulations correspond very well with the NSOM results. We clearly see that the
parallel-polarized light exhibits double periodicity (two intensity peaks per antenna
pair), while the perpendicularly polarized light exhibits single periodicity. The double
115
periodicity of the parallel-polarized light can be attributed almost entirely to the |Ez|2
component of the field (data not shown). This is indicative of diffraction coming
from the antenna structures, rather than the antenna hot-spot transfer that we were
seeking. However, the intensity profile still shows subwavelength confinement on the
far side of the superlens.
To further validate this hypothesis, scans were taken at Purdue with unpolarized,
633nm light at the edge of the antenna array, as seen in Fig 9.14. The left image
of Fig. 9.14 shows the AFM height profile that was measured concurrently with the
NSOM scan. While the antennas cover only about 40% of the image, the intensity
pattern extends throughout the whole NSOM image. This further indicates that a
propagating diffraction mode dominates the near-field intensity profile on the far side
of the superlens.
9.6.3 Reference Sample
Fig. 9.15 shows the experimental NSOM and corresponding simulation images for
the reference sample, which has only a dielectric spacer above the nanoantenna arrays.
In this case, both the simulations and the NSOM results were found using 660nm in-
cident light. The FDTD simulations for the reference sample correspond reasonably
well with the NSOM results. The simulation for parallel-polarized light shows a very
wide and ill-defined profile in the high-intensity stripes, and the NSOM results show
similar results with relatively wide, poorly defined stripes. For the case of perpendic-
ularly polarized incident light, the NSOM results clearly show high intensities for the
areas adjacent to the individual antenna pairs. These results also correspond quite
well with the FDTD simulation, where strong intensities are predicted for the areas
adjacent to the antenna pairs.
116
9.7 Conclusions and Final Remarks
We have studied lamellar superlens designs using experimental measurements and
advanced numerical simulations. For this work, three different sample types were
prepared: bare antennas, antennas with a silver superlens, and antennas with a ref-
erence dielectric layer. Each sample was designed, fabricated, and characterized to
ascertain how the enhanced-field hot spot created by the antennas was translated
to the top side of the sample. In-depth FDTD simulations were performed to com-
pare with experimental measurements, and after analyzing the results, we conclude
that the superlens is not strongly transferring the antenna hot spot to the top side
of the sample. However, the superlens does provide the unintended consequence of
transferring a diffraction grating to the far side of the superlens, and this still pro-
vides subwavelength confinement of energy that could be used in enhanced sensing
applications or other devices.
In fact, this phenomenon provides a method of tailoring the localized, subwave-
length near-field enhancement of a superlens-translated intensity distribution. By
adjusting the sizes, shapes and periodicities of the nanoantenna array, we can apply
a genetic algorithm to optimize the near-field intensity distribution on the far side
of a superlens. In doing so, we can match the final near-field intensity pattern to a
specific application such as sensing or nonlinear-optical studies. This will be our next
step in our research on nanoantenna-superlens combinations.
117
Fig. 9.11. Representative FDTD near-field intensity maps. Thesemaps were calculated for the bare antenna sample with 620nm il-luminating light at the parallel polarization (left column) and theperpendicular polarization (right column). The maps show the in-tensity patterns 10 nm above the sample, averaged in a 150nm radiuscircle, and plotted for each field component. The corresponding inten-sity scales (arbitrary units) are also shown. The x- and z-componentsdominate in the parallel polarization, but the y-component dominatesin the perpendicular polarization.
118
Fig. 9.12. NSOM scans and corresponding total near-field intensitysimulations for the bare antenna sample in both polarizations and atan incident wavelength of 620 nm.
119
Fig. 9.13. NSOM scans (upper panels) and corresponding total near-field intensity simulations (lower panels) for the superlens sample inboth polarizations and at an incident wavelength of 680 nm.
Fig. 9.14. NSOM scans with unpolarized light at the edge of an an-tenna array. The image on the left shows the topography (heightprofile) of the sample. The antennas cover roughly 40% of the image.The image on the right shows the corresponding NSOM intensity pro-file of the same region. The intensity pattern continues beyond thearray, indicating a propagating, diffraction-based mode.
120
Fig. 9.15. NSOM scans (upper panels) and corresponding total near-field intensity simulations (lower panels) for the reference sample inboth polarizations and at an incident wavelength of 660 nm.
LIST OF REFERENCES
121
LIST OF REFERENCES
[1] E. Ozbay, “Plasmonics: merging photonics and electronics at nanoscale dimen-sions,” science, vol. 311, no. 5758, pp. 189–193, 2006.
[2] R. Ritchie, “Plasma losses by fast electrons in thin films,” Physical Review,vol. 106, no. 5, p. 874, 1957.
[3] W. L. Barnes, A. Dereux, T. W. Ebbesen, et al., “Surface plasmon subwave-length optics,” Nature, vol. 424, no. 6950, pp. 824–830, 2003.
[4] S. A. Maier and H. A. Atwater, “Plasmonics: Localization and guiding of elec-tromagnetic energy in metal/dielectric structures,” Journal of Applied Physics,vol. 98, no. 1, pp. 011101–011101, 2005.
[5] S. Lal, S. Link, and N. J. Halas, “Nano-optics from sensing to waveguiding,”Nature photonics, vol. 1, no. 11, pp. 641–648, 2007.
[6] V. G. Veselago et al., “The electrodynamics of substances with simultaneouslynegative values of ε and μ,” Physics-Uspekhi, vol. 10, no. 4, pp. 509–514, 1968.
[7] J. B. Pendry, “Negative refraction makes a perfect lens,” Physical review letters,vol. 85, no. 18, pp. 3966–3969, 2000.
[8] A. V. Kildishev and V. M. Shalaev, “Engineering space for light via transfor-mation optics,” Optics letters, vol. 33, no. 1, pp. 43–45, 2008.
[9] W. Cai and V. Shalaev, Optical metamaterials: fundamentals and applications.Springer, 2009.
[10] A. Ward and J. Pendry, “Refraction and geometry in maxwell’s equations,”Journal of Modern Optics, vol. 43, no. 4, pp. 773–793, 1996.
[11] J. B. Pendry, D. Schurig, and D. R. Smith, “Controlling electromagnetic fields,”Science, vol. 312, no. 5781, pp. 1780–1782, 2006.
[12] V. M. Shalaev, “Transforming light,” Science, vol. 322, no. 5900, pp. 384–386,2008.
[13] S. A. Maier, P. G. Kik, H. A. Atwater, S. Meltzer, E. Harel, B. E. Koel, andA. A. Requicha, “Local detection of electromagnetic energy transport below thediffraction limit in metal nanoparticle plasmon waveguides,” Nature materials,vol. 2, no. 4, pp. 229–232, 2003.
[14] S. I. Bozhevolnyi, V. S. Volkov, E. Devaux, J.-Y. Laluet, and T. W. Ebbesen,“Channel plasmon subwavelength waveguide components including interferom-eters and ring resonators,” Nature, vol. 440, no. 7083, pp. 508–511, 2006.
122
[15] W. Rechberger, A. Hohenau, A. Leitner, J. Krenn, B. Lamprecht, andF. Aussenegg, “Optical properties of two interacting gold nanoparticles,” OpticsCommunications, vol. 220, no. 1, pp. 137–141, 2003.
[16] D. P. Fromm, A. Sundaramurthy, P. J. Schuck, G. Kino, and W. Moerner,“Gap-dependent optical coupling of single bowtie nanoantennas resonant in thevisible,” Nano Letters, vol. 4, no. 5, pp. 957–961, 2004.
[17] T. Atay, J.-H. Song, and A. V. Nurmikko, “Strongly interacting plasmonnanoparticle pairs: from dipole-dipole interaction to conductively coupledregime,” Nano Letters, vol. 4, no. 9, pp. 1627–1631, 2004.
[18] P. Muhlschlegel, H.-J. Eisler, O. Martin, B. Hecht, and D. Pohl, “Resonantoptical antennas,” Science, vol. 308, no. 5728, pp. 1607–1609, 2005.
[19] A. Sundaramurthy, K. Crozier, G. Kino, D. Fromm, P. Schuck, and W. Moerner,“Field enhancement and gap-dependent resonance in a system of two opposingtip-to-tip au nanotriangles,” Physical Review B, vol. 72, no. 16, p. 165409, 2005.
[20] A. K. Sarychev, G. Shvets, and V. M. Shalaev, “Magnetic plasmon resonance,”Physical Review E, vol. 73, no. 3, p. 036609, 2006.
[21] A. Sundaramurthy, P. J. Schuck, N. R. Conley, D. P. Fromm, G. S. Kino, andW. Moerner, “Toward nanometer-scale optical photolithography: utilizing thenear-field of bowtie optical nanoantennas,” Nano letters, vol. 6, no. 3, pp. 355–360, 2006.
[22] O. Muskens, V. Giannini, J. Sanchez-Gil, and J. G. Rivas, “Strong enhancementof the radiative decay rate of emitters by single plasmonic nanoantennas,” Nanoletters, vol. 7, no. 9, pp. 2871–2875, 2007.
[23] R. M. Bakker, V. P. Drachev, Z. Liu, H.-K. Yuan, R. H. Pedersen, A. Boltasseva,J. Chen, J. Irudayaraj, A. V. Kildishev, and V. M. Shalaev, “Nanoantennaarray-induced fluorescence enhancement and reduced lifetimes,” New Journalof Physics, vol. 10, no. 12, p. 125022, 2008.
[24] R. M. Bakker, H.-K. Yuan, Z. Liu, V. P. Drachev, A. V. Kildishev, V. M.Shalaev, R. H. Pedersen, S. Gresillon, and A. Boltasseva, “Enhanced localizedfluorescence in plasmonic nanoantennae,” Applied Physics Letters, vol. 92, no. 4,pp. 043101–043101, 2008.
[25] N. Fang and X. Zhang, “Imaging properties of a metamaterial superlens,” Ap-plied Physics Letters, vol. 82, no. 2, pp. 161–163, 2003.
[26] N. Fang, H. Lee, C. Sun, and X. Zhang, “Sub–diffraction-limited optical imagingwith a silver superlens,” Science, vol. 308, no. 5721, pp. 534–537, 2005.
[27] D. O. Melville, R. J. Blaikie, et al., “Super-resolution imaging through a planarsilver layer,” Opt. Express, vol. 13, no. 6, pp. 2127–2134, 2005.
[28] W. Cai, D. A. Genov, and V. M. Shalaev, “Superlens based on metal-dielectriccomposites,” Physical Review B, vol. 72, no. 19, p. 193101, 2005.
[29] D. Schurig, J. Mock, B. Justice, S. A. Cummer, J. Pendry, A. Starr, andD. Smith, “Metamaterial electromagnetic cloak at microwave frequencies,” Sci-ence, vol. 314, no. 5801, pp. 977–980, 2006.
123
[30] U. Leonhardt, “Optical conformal mapping,” Science, vol. 312, no. 5781,pp. 1777–1780, 2006.
[31] W. Cai, U. K. Chettiar, A. V. Kildishev, and V. M. Shalaev, “Optical cloakingwith metamaterials,” Nature photonics, vol. 1, no. 4, pp. 224–227, 2007.
[32] A. Alu and N. Engheta, “Multifrequency optical invisibility cloak with layeredplasmonic shells,” Physical review letters, vol. 100, no. 11, p. 113901, 2008.
[33] Z. Jacob, L. V. Alekseyev, and E. Narimanov, “Optical hyperlens: Far-fieldimaging beyond the diffraction limit,” Optics express, vol. 14, no. 18, pp. 8247–8256, 2006.
[34] A. Salandrino and N. Engheta, “Far-field subdiffraction optical microscopy us-ing metamaterial crystals: Theory and simulations,” Physical Review B, vol. 74,no. 7, p. 075103, 2006.
[35] Z. Liu, H. Lee, Y. Xiong, C. Sun, and X. Zhang, “Far-field optical hyper-lens magnifying sub-diffraction-limited objects,” Science, vol. 315, no. 5819,pp. 1686–1686, 2007.
[36] I. I. Smolyaninov, Y.-J. Hung, and C. C. Davis, “Magnifying superlens in thevisible frequency range,” Science, vol. 315, no. 5819, pp. 1699–1701, 2007.
[37] D. Schurig, J. Pendry, and D. Smith, “Transformation-designed optical ele-ments,” Optics Express, vol. 15, no. 22, pp. 14772–14782, 2007.
[38] Y. Xiong, Z. Liu, and X. Zhang, “A simple design of flat hyperlens for lithog-raphy and imaging with half-pitch resolution down to 20 nm,” Applied PhysicsLetters, vol. 94, no. 20, pp. 203108–203108, 2009.
[39] P. B. Johnson and R. Christy, “Optical constants of the noble metals,” PhysicalReview B, vol. 6, no. 12, p. 4370, 1972.
[40] J. Marton and B. Jordan, “Optical properties of aggregated metal systems:Interband transitions,” Physical Review B, vol. 15, no. 4, p. 1719, 1977.
[41] A. Sudarkin and P. Demkovich, “Excitation of surface electromagnetic waves onthe boundary of a metal with an amplifying medium,” Sov. Phys. Tech. Phys,vol. 34, pp. 764–766, 1989.
[42] C. Sirtori, C. Gmachl, F. Capasso, D. L. Sivco, A. L. Hutchinson, A. Y. Cho,et al., “Long-wavelength (λ 8–11.5 μm) semiconductor lasers with waveguidesbased on surface plasmons,” Optics letters, vol. 23, no. 17, pp. 1366–1368, 1998.
[43] M. Nezhad, K. Tetz, and Y. Fainman, “Gain assisted propagation of surfaceplasmon polaritons on planar metallic waveguides,” Optics Express, vol. 12,no. 17, pp. 4072–4079, 2004.
[44] A. Tredicucci, C. Gmachl, F. Capasso, A. L. Hutchinson, D. L. Sivco, andA. Y. Cho, “Single-mode surface-plasmon laser,” Applied physics letters, vol. 76,no. 16, pp. 2164–2166, 2000.
[45] D. J. Bergman and M. I. Stockman, “Surface plasmon amplification by stimu-lated emission of radiation: quantum generation of coherent surface plasmonsin nanosystems,” Physical review letters, vol. 90, no. 2, p. 27402, 2003.
124
[46] N. Lawandy, “Localized surface plasmon singularities in amplifying media,”Applied physics letters, vol. 85, no. 21, pp. 5040–5042, 2004.
[47] J. Seidel, S. Grafstrom, and L. Eng, “Stimulated emission of surface plasmonsat the interface between a silver film and an optically pumped dye solution,”Physical review letters, vol. 94, no. 17, p. 177401, 2005.
[48] M. Noginov, G. Zhu, M. Bahoura, J. Adegoke, C. Small, B. Ritzo, V. Drachev,and V. Shalaev, “Enhancement of surface plasmons in an ag aggregate by opticalgain in a dielectric medium,” Optics letters, vol. 31, no. 20, pp. 3022–3024, 2006.
[49] T. A. Klar, A. V. Kildishev, V. P. Drachev, and V. M. Shalaev, “Negative-indexmetamaterials: Going optical,” Selected Topics in Quantum Electronics, IEEEJournal of, vol. 12, no. 6, pp. 1106–1115, 2006.
[50] M. Noginov, V. Podolskiy, G. Zhu, M. Mayy, M. Bahoura, J. Adegoke, B. Ritzo,and K. Reynolds, “Compensation of loss in propagating surface plasmon po-lariton by gain in adjacent dielectric medium,” Optics express, vol. 16, no. 2,pp. 1385–1392, 2008.
[51] M. Noginov, G. Zhu, M. Mayy, B. Ritzo, N. Noginova, and V. Podolskiy, “Stim-ulated emission of surface plasmon polaritons,” Physical review letters, vol. 101,no. 22, p. 226806, 2008.
[52] M. Ambati, S. H. Nam, E. Ulin-Avila, D. A. Genov, G. Bartal, and X. Zhang,“Observation of stimulated emission of surface plasmon polaritons,” Nano let-ters, vol. 8, no. 11, pp. 3998–4001, 2008.
[53] N. I. Zheludev, S. Prosvirnin, N. Papasimakis, and V. Fedotov, “Lasing spaser,”Nature Photonics, vol. 2, no. 6, pp. 351–354, 2008.
[54] M. Noginov, G. Zhu, A. Belgrave, R. Bakker, V. Shalaev, E. Narimanov,S. Stout, E. Herz, T. Suteewong, and U. Wiesner, “Demonstration of a spaser-based nanolaser,” Nature, vol. 460, no. 7259, pp. 1110–1112, 2009.
[55] R. F. Oulton, V. J. Sorger, T. Zentgraf, R.-M. Ma, C. Gladden, L. Dai, G. Bar-tal, and X. Zhang, “Plasmon lasers at deep subwavelength scale,” Nature,vol. 461, no. 7264, pp. 629–632, 2009.
[56] G. V. Naik, V. M. Shalaev, and A. Boltasseva, “Alternative plasmonic materials:beyond gold and silver,” Advanced Materials, vol. 25, no. 24, pp. 3264–3294,2013.
[57] V. P. Drachev, U. K. Chettiar, A. V. Kildishev, H.-K. Yuan, W. Cai, andV. M. Shalaev, “The ag dielectric function in plasmonic metamaterials,” OpticsExpress, vol. 16, no. 2, pp. 1186–1195, 2008.
[58] N. Ashcroft and N. Mermin, Solid Stale Physics. Saunders College, Philadel-phia, 1976.
[59] H. Ehrenreich and H. Philipp, “Optical properties of ag and cu,” Physical Re-view, vol. 128, no. 4, p. 1622, 1962.
[60] B. Cooper, H. Ehrenreich, and H. Philipp, “Optical properties of noble metals.ii.,” Physical Review, vol. 138, no. 2A, p. A494, 1965.
125
[61] H. Ehrenreich, H. Philipp, and B. Segall, “Optical properties of aluminum,”Physical Review, vol. 132, no. 5, p. 1918, 1963.
[62] R. LaVilla and H. Mendlowitz, “Optical constants of aluminum in vacuumultraviolet,” Physical Review Letters, vol. 9, no. 4, pp. 149–150, 1962.
[63] H. Hovel, S. Fritz, A. Hilger, U. Kreibig, and M. Vollmer, “Width of clusterplasmon resonances: Bulk dielectric functions and chemical interface damping,”Physical Review B, vol. 48, no. 24, p. 18178, 1993.
[64] B. N. J. Persson, “Surface resistivity and vibrational damping in adsorbed lay-ers,” Phys. Rev. B, vol. 44, pp. 3277–3296, Aug 1991.
[65] M. Dressel and G. Gruner, Electrodynamics of solids: optical properties of elec-trons in matter. Cambridge University Press, 2002.
[66] A. D. Rakic, A. B. Djurisic, J. M. Elazar, and M. L. Majewski, “Optical proper-ties of metallic films for vertical-cavity optoelectronic devices,” Applied Optics,vol. 37, no. 22, pp. 5271–5283, 1998.
[67] D. Thomas, J. Hopfield, and C. Frosch, “Isoelectronic traps due to nitrogen ingallium phosphide,” Physical Review Letters, vol. 15, no. 22, pp. 857–860, 1965.
[68] C. Kittel and P. McEuen, Introduction to solid state physics, vol. 7. Wiley NewYork, 1996.
[69] J. Hopfield, “Theory of the contribution of excitons to the complex dielectricconstant of crystals,” Physical Review, vol. 112, no. 5, p. 1555, 1958.
[70] J. D. Dow and D. Redfield, “Electroabsorption in semiconductors: the excitonicabsorption edge,” Physical Review B, vol. 1, no. 8, p. 3358, 1970.
[71] W. Dumke, “Optical transitions involving impurities in semiconductors,” Phys-ical Review, vol. 132, no. 5, p. 1998, 1963.
[72] G. Dolling, M. Wegener, C. M. Soukoulis, and S. Linden, “Negative-index meta-material at 780 nm wavelength,” Optics letters, vol. 32, no. 1, pp. 53–55, 2007.
[73] T. W. Ebbesen, H. Lezec, H. Ghaemi, T. Thio, and P. Wolff, “Extraordinaryoptical transmission through sub-wavelength hole arrays,” Nature, vol. 391,no. 6668, pp. 667–669, 1998.
[74] V. M. Shalaev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P.Drachev, and A. V. Kildishev, “Negative index of refraction in optical metama-terials,” Optics Letters, vol. 30, no. 24, pp. 3356–3358, 2005.
[75] S. A. Maier, Plasmonics: Fundamentals and Applications: Fundamentals andApplications. Springer, 2007.
[76] P. Tobiska, O. Hugon, A. Trouillet, and H. Gagnaire, “An integrated optic hy-drogen sensor based on spr on palladium,” Sensors and Actuators B: Chemical,vol. 74, no. 1, pp. 168–172, 2001.
[77] S. Baldelli, A. S. Eppler, E. Anderson, Y.-R. Shen, and G. A. Somorjai, “Surfaceenhanced sum frequency generation of carbon monoxide adsorbed on platinumnanoparticle arrays,” The Journal of Chemical Physics, vol. 113, p. 5432, 2000.
126
[78] E. D. Palik, Handbook of optical constants of solids, vol. 3. Academic press,1998.
[79] M. Blaber, M. Arnold, N. Harris, M. Ford, and M. Cortie, “Plasmon absorptionin nanospheres: A comparison of sodium, potassium, aluminium, silver andgold,” Physica B: Condensed Matter, vol. 394, no. 2, pp. 184–187, 2007.
[80] T. Lewowski, “Photoelectron spectroscopy of thin discontinuous silver filmsdeposited onto a sapphire substrate, near the percolation threshold,” Thin solidfilms, vol. 259, no. 1, pp. 53–58, 1995.
[81] H. Wei and H. Eilers, “From silver nanoparticles to thin films: Evolution of mi-crostructure and electrical conduction on glass substrates,” Journal of Physicsand Chemistry of Solids, vol. 70, no. 2, pp. 459–465, 2009.
[82] T. Oates and A. Mucklich, “Evolution of plasmon resonances during plasmadeposition of silver nanoparticles,” Nanotechnology, vol. 16, no. 11, p. 2606,2005.
[83] D. D. Smith, Y. Yoon, R. W. Boyd, J. K. Campbell, L. A. Baker, R. M. Crooks,and M. George, “Z-scan measurement of the nonlinear absorption of a thin goldfilm,” Journal of applied physics, vol. 86, no. 11, pp. 6200–6205, 1999.
[84] Y. Yagil, P. Gadenne, C. Julien, and G. Deutscher, “Optical properties of thinsemicontinuous gold films over a wavelength range of 2.5 to 500 μm,” PhysicalReview B, vol. 46, no. 4, p. 2503, 1992.
[85] K. Seal, M. A. Nelson, Z. C. Ying, D. A. Genov, A. K. Sarychev, and V. M.Shalaev, “Metal coverage dependence of local optical properties of semicontinu-ous metallic films,” journal of modern optics, vol. 49, no. 14-15, pp. 2423–2435,2002.
[86] A. K. Sarychev and V. M. Shalaev, Electrodynamics of metamaterials. WorldScientific Publishing Company Incorporated, 2007.
[87] G. H. Chan, J. Zhao, E. M. Hicks, G. C. Schatz, and R. P. Van Duyne, “Plas-monic properties of copper nanoparticles fabricated by nanosphere lithography,”Nano Letters, vol. 7, no. 7, pp. 1947–1952, 2007.
[88] C. Langhammer, M. Schwind, B. Kasemo, and I. Zoric, “Localized surface plas-mon resonances in aluminum nanodisks,” Nano letters, vol. 8, no. 5, pp. 1461–1471, 2008.
[89] G. H. Chan, J. Zhao, G. C. Schatz, and R. P. V. Duyne, “Localized surfaceplasmon resonance spectroscopy of triangular aluminum nanoparticles,” TheJournal of Physical Chemistry C, vol. 112, no. 36, pp. 13958–13963, 2008.
[90] J. Quail, J. Rako, and H. Simon, “Long-range surface-plasmon modes in silverand aluminum films,” Optics letters, vol. 8, no. 7, pp. 377–379, 1983.
[91] J. R. Lakowicz, C. D. Geddes, I. Gryczynski, J. Malicka, Z. Gryczynski,K. Aslan, J. Lukomska, E. Matveeva, J. Zhang, R. Badugu, et al., “Advances insurface-enhanced fluorescence,” Journal of fluorescence, vol. 14, no. 4, pp. 425–441, 2004.
127
[92] K. Ray, M. H. Chowdhury, and J. R. Lakowicz, “Aluminum nanostructuredfilms as substrates for enhanced fluorescence in the ultraviolet-blue spectralregion,” Analytical chemistry, vol. 79, no. 17, pp. 6480–6487, 2007.
[93] T. Dorfer, M. Schmitt, and J. Popp, “Deep-uv surface-enhanced raman scat-tering,” Journal of Raman Spectroscopy, vol. 38, no. 11, pp. 1379–1382, 2007.
[94] A. Taguchi, N. Hayazawa, K. Furusawa, H. Ishitobi, and S. Kawata, “Deep-uvtip-enhanced raman scattering,” Journal of Raman Spectroscopy, vol. 40, no. 9,pp. 1324–1330, 2009.
[95] V. Guritanu, A. Kuzmenko, D. Van der Marel, S. Kazakov, N. Zhigadlo, andJ. Karpinski, “Anisotropic optical conductivity and two colors of mgb {2},”Physical Review B, vol. 73, no. 10, p. 104509, 2006.
[96] Y. Fudamoto and S. Lee, “Anisotropic electrodynamics of mgb {2} detectedby optical reflectance,” Physical Review B, vol. 68, no. 18, p. 184514, 2003.
[97] R. A. Kaindl, M. A. Carnahan, J. Orenstein, D. S. Chemla, H. M. Christen,H.-Y. Zhai, M. Paranthaman, and D. H. Lowndes, “Far-infrared optical conduc-tivity gap in superconducting mgb {2} films,” Physical review letters, vol. 88,no. 2, p. 27003, 2001.
[98] J. Tu, G. Carr, V. Perebeinos, C. Homes, M. Strongin, P. Allen, W. Kang, E.-M.Choi, H.-J. Kim, and S.-I. Lee, “Optical properties of c-axis oriented supercon-ducting mgb {2} films,” Physical review letters, vol. 87, no. 27, p. 277001,2001.
[99] M.-O. Mun, Y. J. Kim, Y. Park, J. H. Kim, S. Moon, H. Lee, H. Kim, andB. Oh, “Normal-state optical response functions of mgb 2 superconductor,”Journal of superconductivity, vol. 15, no. 5, pp. 475–477, 2002.
[100] J.-T. Lue, S.-J. Mu, and I.-C. Wu, “Ellipsometry and structure studies ofchromium, molybdenum, and platinum silicides,” Physical Review B, vol. 36,no. 3, pp. 1657–1661, 1987.
[101] A. Borghesi, L. Nosenzo, A. Piaggi, G. Guizzetti, C. Nobili, and G. Ottaviani,“Optical properties of tantalum disilicide thin films,” Physical Review B, vol. 38,no. 15, p. 10937, 1988.
[102] A. Borghesi, A. Piaggi, G. Guizzetti, F. Nava, and M. Bacchetta, “Opticalproperties of vanadium silicide polycrystalline films,” Physical Review B, vol. 40,no. 5, p. 3249, 1989.
[103] M. Amiotti, A. Borghesi, G. Guizzetti, and F. Nava, “Optical properties ofpolycrystalline nickel silicides,” Physical Review B, vol. 42, no. 14, p. 8939,1990.
[104] V. Antonov, V. N. Antonov, O. Jepsen, O. Andersen, A. Borghesi, C. Bosio,F. Marabelli, A. Piaggi, G. Guizzetti, and F. Nava, “Optical properties of wsi{2},” Physical Review B, vol. 44, no. 16, p. 8437, 1991.
[105] Z.-C. Wu, E. Arakawa, J. Jimenez, and L. Schowalter, “Optical properties ofepitaxial cosi {2} on si from 0.062 to 22.3 ev,” Physical Review B, vol. 47,no. 8, p. 4356, 1993.
128
[106] D. Bobb, G. Zhu, M. Mayy, A. Gavrilenko, P. Mead, V. Gavrilenko, andM. Noginov, “Engineering of low-loss metal for nanoplasmonic and metamate-rials applications,” Applied Physics Letters, vol. 95, no. 15, pp. 151102–151102,2009.
[107] M. Blaber, M. Arnold, and M. Ford, “Optical properties of intermetallic com-pounds from first principles calculations: a search for the ideal plasmonic ma-terial,” Journal of Physics: Condensed Matter, vol. 21, no. 14, p. 144211, 2009.
[108] M. Zwilling, P. Schmidt, and A. Weiss, “Experimental and theoretical studiesof optical properties on alloys of the intermetallic systems li2ag2- x in x andli2cd2- x in x,” Applied physics, vol. 16, no. 3, pp. 255–269, 1978.
[109] K. H. Kim, K. C. Park, and D. Y. Ma, “Structural, electrical and opticalproperties of aluminum doped zinc oxide films prepared by radio frequencymagnetron sputtering,” Journal of Applied Physics, vol. 81, no. 12, pp. 7764–7772, 1997.
[110] I. Hamberg and C. G. Granqvist, “Evaporated sn-doped in2o3 films: basic opti-cal properties and applications to energy-efficient windows,” Journal of AppliedPhysics, vol. 60, no. 11, pp. R123–R160, 1986.
[111] A. J. Hoffman, L. Alekseyev, S. S. Howard, K. J. Franz, D. Wasserman, V. A.Podolskiy, E. E. Narimanov, D. L. Sivco, and C. Gmachl, “Negative refractionin semiconductor metamaterials,” Nature materials, vol. 6, no. 12, pp. 946–950,2007.
[112] J. A. Schuller, R. Zia, T. Taubner, and M. L. Brongersma, “Dielectric metama-terials based on electric and magnetic resonances of silicon carbide particles,”Physical review letters, vol. 99, no. 10, p. 107401, 2007.
[113] T. Taubner, D. Korobkin, Y. Urzhumov, G. Shvets, and R. Hillenbrand, “Near-field microscopy through a sic superlens,” Science, vol. 313, no. 5793, pp. 1595–1595, 2006.
[114] C. Wolfe and G. Stillman, “Self-compensation of donors in high-purity gaas,”Applied Physics Letters, vol. 27, no. 10, pp. 564–567, 2008.
[115] X. Cao, C. Abernathy, R. Singh, S. Pearton, M. Fu, V. Sarvepalli, J. Sekhar,J. Zolper, D. Rieger, J. Han, et al., “Ultrahigh si+ implant activation efficiencyin gan using a high-temperature rapid thermal process system,” Applied physicsletters, vol. 73, no. 2, pp. 229–231, 1998.
[116] P. Robusto and R. Braunstein, “Optical measurements of the surface plasmonof indium-tin oxide,” physica status solidi (a), vol. 119, no. 1, pp. 155–168, 1990.
[117] M. Xu, M. Alam, A. Zilkie, K. Zeaiter, and J. Aitchison, “Surface plasmonpolaritons mediated by ito at near infrared wavelength,” in Lasers and Electro-Optics, 2008 and 2008 Conference on Quantum Electronics and Laser Science.CLEO/QELS 2008. Conference on, pp. 1–2, IET, 2008.
[118] F. Michelotti, L. Dominici, E. Descrovi, N. Danz, and F. Menchini, “Thicknessdependence of surface plasmon polariton dispersion in transparent conductingoxide films at 1.55 μm,” Optics letters, vol. 34, no. 6, pp. 839–841, 2009.
129
[119] C. Rhodes, M. Cerruti, A. Efremenko, M. Losego, D. Aspnes, J.-P. Maria, andS. Franzen, “Dependence of plasmon polaritons on the thickness of indium tinoxide thin films,” Journal of Applied Physics, vol. 103, no. 9, p. 093108, 2008.
[120] S. Franzen, “Surface plasmon polaritons and screened plasma absorption in in-dium tin oxide compared to silver and gold,” The Journal of Physical ChemistryC, vol. 112, no. 15, pp. 6027–6032, 2008.
[121] S. H. Brewer and S. Franzen, “Erratum to optical properties of indium tin oxideand fluorine-doped tin oxide surfaces: correlation of reflectivity, skin depth,and plasmon frequency with conductivity:[j. alloys comp. 338 (2002) 73–79],”Journal of Alloys and Compounds, vol. 343, no. 1, p. 244, 2002.
[122] A. Solieman and M. A. Aegerter, “Modeling of optical and electrical propertiesof in¡ sub¿ 2¡/sub¿ o¡ sub¿ 3¡/sub¿: Sn coatings made by various techniques,”Thin Solid Films, vol. 502, no. 1, pp. 205–211, 2006.
[123] K. Ellmer and R. Mientus, “Carrier transport in polycrystalline ito and zno: Alii: the influence of grain barriers and boundaries,” Thin Solid Films, vol. 516,no. 17, pp. 5829–5835, 2008.
[124] F. Lai, L. Lin, R. Gai, Y. Lin, and Z. Huang, “Determination of optical con-stants and thicknesses of in2o3:sn films from transmittance data,” Thin SolidFilms, vol. 515, no. 18, pp. 7387 – 7392, 2007.
[125] M. Hiramatsu, K. Imaeda, N. Horio, and M. Nawata, “Transparent conductingzno thin films prepared by xecl excimer laser ablation,” Journal of VacuumScience & Technology A, vol. 16, no. 2, pp. 669–673, 1998.
[126] H. Kim, A. Pique, J. Horwitz, H. Murata, Z. Kafafi, C. Gilmore, and D. Chrisey,“Effect of aluminum doping on zinc oxide thin films grown by pulsed laser de-position for organic light-emitting devices,” Thin Solid Films, vol. 377, pp. 798–802, 2000.
[127] H. Agura, A. Suzuki, T. Matsushita, T. Aoki, and M. Okuda, “Low resistivitytransparent conducting al-doped zno films prepared by pulsed laser deposition,”Thin Solid Films, vol. 445, no. 2, pp. 263–267, 2003.
[128] A. Singh, R. Mehra, N. Buthrath, A. Wakahara, and A. Yoshida, “Highly con-ductive and transparent aluminum-doped zinc oxide thin films prepared bypulsed laser deposition in oxygen ambient,” Journal of Applied Physics, vol. 90,no. 11, pp. 5661–5665, 2001.
[129] J. Lu, Z. Ye, Y. Zeng, L. Zhu, L. Wang, J. Yuan, B. Zhao, and Q. Liang,“Structural, optical, and electrical properties of (zn, al) o films over a widerange of compositions,” Journal of Applied Physics, vol. 100, no. 7, p. 073714,2006.
[130] M. Yoon, S. Lee, H. Park, H. Kim, and M. Jang, “Solid solubility limits of gaand al in zno,” Journal of materials science letters, vol. 21, no. 21, pp. 1703–1704, 2002.
[131] K. S. Novoselov, A. K. Geim, S. Morozov, D. Jiang, Y. Zhang, S. Dubonos,I. Grigorieva, and A. Firsov, “Electric field effect in atomically thin carbonfilms,” science, vol. 306, no. 5696, pp. 666–669, 2004.
130
[132] K. Novoselov, A. K. Geim, S. Morozov, D. Jiang, M. Katsnelson, I. Grigorieva,S. Dubonos, and A. Firsov, “Two-dimensional gas of massless dirac fermions ingraphene,” nature, vol. 438, no. 7065, pp. 197–200, 2005.
[133] F. Schedin, A. Geim, S. Morozov, E. Hill, P. Blake, M. Katsnelson, andK. Novoselov, “Detection of individual gas molecules adsorbed on graphene,”Nature materials, vol. 6, no. 9, pp. 652–655, 2007.
[134] K. V. Emtsev, A. Bostwick, K. Horn, J. Jobst, G. L. Kellogg, L. Ley, J. L.McChesney, T. Ohta, S. A. Reshanov, J. Rohrl, et al., “Towards wafer-sizegraphene layers by atmospheric pressure graphitization of silicon carbide,” Na-ture materials, vol. 8, no. 3, pp. 203–207, 2009.
[135] F. Stern, “Polarizability of a two-dimensional electron gas,” Physical ReviewLetters, vol. 18, pp. 546–548, 1967.
[136] E. Hwang and S. D. Sarma, “Dielectric function, screening, and plasmons intwo-dimensional graphene,” Physical Review B, vol. 75, no. 20, p. 205418, 2007.
[137] S. D. Sarma and E. Hwang, “Collective modes of the massless dirac plasma,”Physical review letters, vol. 102, no. 20, p. 206412, 2009.
[138] V. Ryzhii, A. Satou, and T. Otsuji, “Plasma waves in two-dimensional electron-hole system in gated graphene heterostructures,” Journal of applied physics,vol. 101, no. 2, pp. 024509–024509, 2007.
[139] H. Wang, J. H. Strait, P. A. George, S. Shivaraman, V. B. Shields, M. Chan-drashekhar, J. Hwang, F. Rana, M. G. Spencer, C. S. Ruiz-Vargas, et al.,“Ultrafast relaxation dynamics of hot optical phonons in graphene,” AppliedPhysics Letters, vol. 96, no. 8, p. 081917, 2010.
[140] V. Ryzhii, M. Ryzhii, A. Satou, T. Otsuji, A. Dubinov, and V. Y. Aleshkin,“Feasibility of terahertz lasing in optically pumped epitaxial multiple graphenelayer structures,” Journal of Applied Physics, vol. 106, no. 8, p. 084507, 2009.
[141] M. Jablan, H. Buljan, and M. Soljacic, “Plasmonics in graphene at infraredfrequencies,” Physical review B, vol. 80, no. 24, p. 245435, 2009.
[142] Z. Li, E. A. Henriksen, Z. Jiang, Z. Hao, M. C. Martin, P. Kim, H. Stormer, andD. N. Basov, “Dirac charge dynamics in graphene by infrared spectroscopy,”Nature Physics, vol. 4, no. 7, pp. 532–535, 2008.
[143] J. D. Jackson and R. F. Fox, “Classical electrodynamics,” American Journal ofPhysics, vol. 67, pp. 841–842, 1999.
[144] F. Wang and Y. R. Shen, “General properties of local plasmons in metal nanos-tructures,” Physical review letters, vol. 97, no. 20, p. 206806, 2006.
[145] P. Berini, “Long-range surface plasmon polaritons,” Advances in Optics andPhotonics, vol. 1, no. 3, pp. 484–588, 2009.
[146] M. D. Arnold and M. G. Blaber, “Optical performance and metallic absorptionin nanoplasmonic systems,” Optics express, vol. 17, no. 5, pp. 3835–3847, 2009.
[147] H. Raether, Surface plasmons on smooth surfaces. Springer, 1988.
131
[148] S. A. Ramakrishna, J. Pendry, M. Wiltshire, and W. Stewart, “Imaging thenear field,” Journal of Modern Optics, vol. 50, no. 9, pp. 1419–1430, 2003.
[149] K. Robbie and M. Brett, “Sculptured thin films and glancing angle deposition:Growth mechanics and applications,” Journal of Vacuum Science & TechnologyA, vol. 15, no. 3, pp. 1460–1465, 1997.
[150] Y. Zhao, D. Ye, G.-C. Wang, and T.-M. Lu, “Designing nanostructures byglancing angle deposition,” in Optical Science and Technology, SPIE’s 48thAnnual Meeting, pp. 59–73, International Society for Optics and Photonics,2003.
[151] K. Robbie, J. Sit, and M. Brett, “Advanced techniques for glancing angle deposi-tion,” Journal of Vacuum Science & Technology B, vol. 16, no. 3, pp. 1115–1122,1998.
[152] M. Y. Shalaginov, S. Ishii, J. Liu, J. Irudayaraj, A. Lagutchev, A. V. Kildi-shev, and V. M. Shalaev, “Broadband enhancement of spontaneous emissionfrom nitrogen-vacancy centers in nanodiamonds by hyperbolic metamaterials,”Applied Physics Letters, vol. 102, no. 17, p. 173114, 2013.
[153] W. D. Newman, C. L. Cortes, and Z. Jacob, “Enhanced and directional single-photon emission in hyperbolic metamaterials,” JOSA B, vol. 30, no. 4, pp. 766–775, 2013.
[154] N. Yu, P. Genevet, M. A. Kats, F. Aieta, J.-P. Tetienne, F. Capasso, andZ. Gaburro, “Light propagation with phase discontinuities: generalized laws ofreflection and refraction,” Science, vol. 334, no. 6054, pp. 333–337, 2011.
[155] F. Aieta, P. Genevet, M. A. Kats, N. Yu, R. Blanchard, Z. Gaburro, and F. Ca-passo, “Aberration-free ultrathin flat lenses and axicons at telecom wavelengthsbased on plasmonic metasurfaces,” Nano letters, vol. 12, no. 9, pp. 4932–4936,2012.
[156] A. V. Kildishev, A. Boltasseva, and V. M. Shalaev, “Planar photonics withmetasurfaces,” Science, vol. 339, no. 6125, 2013.
[157] N. Yu, F. Aieta, P. Genevet, M. A. Kats, Z. Gaburro, and F. Capasso, “A broad-band, background-free quarter-wave plate based on plasmonic metasurfaces,”Nano letters, vol. 12, no. 12, pp. 6328–6333, 2012.
[158] M. A. Kats, P. Genevet, G. Aoust, N. Yu, R. Blanchard, F. Aieta, Z. Gaburro,and F. Capasso, “Giant birefringence in optical antenna arrays with widelytailorable optical anisotropy,” Proceedings of the National Academy of Sciences,vol. 109, no. 31, pp. 12364–12368, 2012.
[159] E. S. Bahaa and C. T. Malvin, “Fundamentals of photonics,” New York/AWILEY-INTERSCIENCE PUBLICATION, 1991.
[160] S. Wilson and M. Hutley, “The optical properties of’moth eye’antireflectionsurfaces,” Journal of Modern Optics, vol. 29, no. 7, pp. 993–1009, 1982.
[161] P. Lalanne, S. Astilean, P. Chavel, E. Cambril, and H. Launois, “Design andfabrication of blazed binary diffractive elements with sampling periods smallerthan the structural cutoff,” JOSA A, vol. 16, no. 5, pp. 1143–1156, 1999.
132
[162] M.-S. L. Lee, S. Bansropun, O. Huet, S. Cassette, B. Loiseaux, A. Wood,C. Sauvan, and P. Lalanne, “Sub-wavelength structures for broadband diffrac-tive optics,” in ICO20: Materials and Nanostructures, pp. 602919–602919, In-ternational Society for Optics and Photonics, 2006.
[163] C. Sauvan, P. Lalanne, and M.-S. L. Lee, “Broadband blazing with artificialdielectrics,” Optics letters, vol. 29, no. 14, pp. 1593–1595, 2004.
[164] M. Kuittinen, J. Turunen, and P. Vahimaa, “Rigorous analysis and optimizationof subwavelength-structured binary dielectric beam deflector gratings,” Journalof Modern Optics, vol. 45, no. 1, pp. 133–142, 1998.
[165] P. Lalanne, J.-C. Rodier, P. H. Chavel, E. Cambril, A. Talneau, and Y. Chen,“Applications of index-gradient artificial dielectrics,” in Optical Science andTechnology, SPIE’s 48th Annual Meeting, pp. 1–7, International Society forOptics and Photonics, 2003.
[166] P. Lalanne and M. Hutley, “The optical properties of artificial media structuredat a subwavelength scale,” Encyclopedia of Optical Engineering, pp. 62–71, 2003.
[167] J. Feng and Z. Zhou, “Polarization beam splitter using a binary blazed gratingcoupler,” Optics letters, vol. 32, no. 12, pp. 1662–1664, 2007.
[168] J. Feng and Z. Zhou, “High efficiency compact grating coupler for integratedoptical circuits,” in Asia-Pacific Optical Communications, pp. 63511H–63511H,International Society for Optics and Photonics, 2006.
[169] P. Lalanne, “Waveguiding in blazed-binary diffractive elements,” JOSA A,vol. 16, no. 10, pp. 2517–2520, 1999.
[170] W. Freese, T. Kampfe, E.-B. Kley, and A. Tunnermann, “Design and fabrica-tion of a highly off-axis binary multi-phase-level computer-generated hologrambased on an effective medium approach,” in SPIE MOEMS-MEMS, pp. 792710–792710, International Society for Optics and Photonics, 2011.
[171] W. Yu, K. Takahara, T. Konishi, T. Yotsuya, and Y. Ichioka, “Fabricationof multilevel phase computer-generated hologram elements based on effectivemedium theory,” Applied optics, vol. 39, no. 20, pp. 3531–3536, 2000.
[172] V. Raulot, B. Serio, P. Gerard, P. Twardowski, and P. Meyrueis, “Modelingof a diffractive micro-lens by an effective medium method,” in SPIE PhotonicsEurope, pp. 77162J–77162J, International Society for Optics and Photonics,2010.
[173] B. Kleemann, “Blazed diffractive optical element and projection objective fora microlithographic projection exposure apparatus,” Aug. 28 2007. US Patent7,262,915.
[174] M.-S. L. Lee, P. Lalanne, J. Rodier, P. Chavel, E. Cambril, and Y. Chen,“Imaging with blazed-binary diffractive elements,” Journal of Optics A: Pureand Applied Optics, vol. 4, no. 5, p. S119, 2002.
[175] D. Fattal, J. Li, Z. Peng, M. Fiorentino, and R. G. Beausoleil, “A silicon lensfor integrated free-space optics,” in Integrated Photonics Research, Silicon andNanophotonics, p. ITuD2, Optical Society of America, 2011.
133
[176] J. N. Farahani, D. W. Pohl, H.-J. Eisler, and B. Hecht, “Single quantum dotcoupled to a scanning optical antenna: a tunable superemitter,” Physical ReviewLetters, vol. 95, no. 1, p. 017402, 2005.
[177] Z. Liu, A. Boltasseva, R. H. Pedersen, R. Bakker, A. V. Kildishev, V. P.Drachev, and V. M. Shalaev, “Plasmonic nanoantenna arrays for the visible,”Metamaterials, vol. 2, no. 1, pp. 45–51, 2008.
[178] K. Kneipp, M. Moskovits, and H. Kneipp, Surface-enhanced Raman scattering:physics and applications, vol. 103. Springer, 2006.
[179] P. A. Belov and Y. Hao, “Subwavelength imaging at optical frequencies using atransmission device formed by a periodic layered metal-dielectric structure oper-ating in the canalization regime,” Physical Review B, vol. 73, no. 11, p. 113110,2006.
[180] B. Wood, J. Pendry, and D. Tsai, “Directed subwavelength imaging using alayered metal-dielectric system,” Physical Review B, vol. 74, no. 11, p. 115116,2006.
[181] R. E. Holt and T. M. Cotton, “Surface-enhanced resonance raman and electro-chemical investigation of glucose oxidase catalysis at a silver electrode,” Journalof the American Chemical Society, vol. 111, no. 8, pp. 2815–2821, 1989.
[182] M. Yang, F. L. Chung, and M. Thompson, “Acoustic network analysis as anovel technique for studying protein adsorption and denaturation at surfaces,”Analytical Chemistry, vol. 65, no. 24, pp. 3713–3716, 1993.
[183] P. Anger, P. Bharadwaj, and L. Novotny, “Enhancement and quenching ofsingle-molecule fluorescence,” Physical review letters, vol. 96, no. 11, p. 113002,2006.
[184] C. Jeppesen, R. B. Nielsen, A. Boltasseva, S. Xiao, N. Mortensen, and A. Kris-tensen, “Thin film ag superlens towards lab-on-a-chip integration,” Optics ex-press, vol. 17, no. 25, pp. 22543–22552, 2009.
[185] A. V. Kildishev, W. Cai, U. K. Chettiar, H.-K. Yuan, A. K. Sarychev, V. P.Drachev, and V. M. Shalaev, “Negative refractive index in optics of metal-dielectric composites,” JOSA B, vol. 23, no. 3, pp. 423–433, 2006.
[186] L. Shi, L. Gao, S. He, and B. Li, “Superlens from metal-dielectric compositesof nonspherical particles,” Physical Review B, vol. 76, no. 4, p. 045116, 2007.
[187] L. Shi, L. Gao, and S. He, “Tunable negative refraction and subwavelengthimaging in the metal-dielectric composites of nonspherical particles,” in Bio-photonics, Nanophotonics and Metamaterials, 2006. Metamaterials 2006. In-ternational Symposium on, pp. 463–466, IEEE, 2006.
[188] P. Aravind, A. Nitzan, and H. Metiu, “The interaction between electromagneticresonances and its role in spectroscopic studies of molecules adsorbed on col-loidal particles or metal spheres,” Surface Science, vol. 110, no. 1, pp. 189–204,1981.
[189] E. Hao and G. C. Schatz, “Electromagnetic fields around silver nanoparticlesand dimers,” The Journal of chemical physics, vol. 120, no. 1, pp. 357–366,2003.
134
[190] R. M. Bakker, A. Boltasseva, Z. Liu, R. H. Pedersen, S. Gresillon, A. V. Kildi-shev, V. P. Drachev, and V. M. Shalaev, “Near-field excitation of nanoantennaresonance,” Optics Express, vol. 15, no. 21, pp. 13682–13688, 2007.
[191] V. Shalaev and M. Stockman, “Optical properties of fractal clusters (suscep-tibility, surface enhanced raman scattering by impurities),” Sov. Phys. JETP,vol. 65, pp. 509–522, 1987.
[192] V. Markel, L. Muratov, M. I. Stockman, and T. F. George, “Theory and nu-merical simulation of optical properties of fractal clusters,” Physical Review B,vol. 43, no. 10, p. 8183, 1991.
[193] V. M. Shalaev, “Electromagnetic properties of small-particle composites,”Physics Reports, vol. 272, no. 2, pp. 61–137, 1996.
[194] V. A. Podolskiy, A. K. Sarychev, E. E. Narimanov, and V. M. Shalaev, “Reso-nant light interaction with plasmonic nanowire systems,” Journal of Optics A:Pure and Applied Optics, vol. 7, no. 2, p. S32, 2005.
[195] U. K. Chettiar, A. V. Kildishev, T. A. Klar, and V. M. Shalaev, “Negativeindex metamaterial combining magnetic resonators with metal films,” Opticsexpress, vol. 14, no. 17, pp. 7872–7877, 2006.
[196] Z. Liu, M. D. Thoreson, A. V. Kildishev, and V. M. Shalaev, “Translationof nanoantenna hot spots by a metal-dielectric composite superlens,” Appliedphysics letters, vol. 95, no. 3, p. 033114, 2009.
[197] R. B. Nielsen, M. Thoreson, W. Chen, A. Kristensen, J. Hvam, V. M. Shalaev,and A. Boltasseva, “Toward superlensing with metal-dielectric composites andmultilayers,” Applied Physics B, vol. 100, pp. 93–100, 2010.
[198] M. D. Thoreson, J. Fang, A. V. Kildishev, L. J. Prokopeva, P. Nyga, U. K.Chettiar, V. M. Shalaev, and V. P. Drachev, “Fabrication and realistic modelingof three-dimensional metal-dielectric composites,” Journal of Nanophotonics,vol. 5, no. 1, pp. 051513–051513, 2011.
[199] P. Chaturvedi and N. X. Fang, “Molecular scale imaging with a multilayersuperlens,” in MRS Proceedings, vol. 919, Cambridge Univ Press, 2006.
[200] E. Shamonina, V. Kalinin, K. Ringhofer, and L. Solymar, “Imaging, compres-sion and poynting vector streamlines for negative permittivity materials,” Elec-tronics Letters, vol. 37, no. 20, pp. 1243–1244, 2001.
[201] K.-H. Su, Q.-H. Wei, X. Zhang, J. Mock, D. R. Smith, and S. Schultz, “In-terparticle coupling effects on plasmon resonances of nanogold particles,” NanoLetters, vol. 3, no. 8, pp. 1087–1090, 2003.
[202] T. W. Ebbesen, C. Genet, and S. I. Bozhevolnyi, “Surface-plasmon circuitry,”Physics Today, vol. 61, no. 5, p. 44, 2008.
[203] V. A. Sychugov, A. V. Tishchenko, B. A. Usievich, and O. Parriaux, “Op-timization and control of grating coupling to or from a silicon-based opticalwaveguide,” Optical Engineering, vol. 35, no. 11, pp. 3092–3100, 1996.
[204] L. J. Prokopeva, J. D. Borneman, and A. V. Kildishev, “Optical dispersionmodels for time-domain modeling of metal-dielectric nanostructures,” Magnet-ics, IEEE Transactions on, vol. 47, no. 5, pp. 1150–1153, 2011.
APPENDICES
135
A. ELECTROMAGNETIC BOUNDARY CONDITIONS
FOR NANOMETER-SCALE CONFINEMENT AT
METAL-DIELECTRIC INTERFACES
This chapter provides a brief outline of how plasmonics is used to confine electromag-
netic waves to a very thin, planar metal interface. The principles examined in this
chapter will be used to describe plasmonic materials and devices in future chapters.
We will begin by exploring the metal / dielectric interface shown in Fig. A.1.
Fig. A.1. Metal / dielectric interface used for surface plasmon polariton excitation.
Let us first examine the TM mode of this wave with the geometry shown in Fig.
A.1. In the region z > 0 (dielectric), we solve for this system first by finding the
general solution for Hy, Ex, and Ez:
Hy = A1eiβxe−k1z (A.1)
Ex = iA1k1
ωε1ε0eiβxe−k1z (A.2)
136
Ez = −A1β
ωε1ε0eiβxe−k1z (A.3)
Likewise, in the region z < 0 (metal), we have:
Hy = A2eiβxe−k2z (A.4)
Ex = −iA2k2
ωε2ε0eiβxe−k2z (A.5)
Ez = −A2β
ωε2ε0eiβxek2z (A.6)
It is important to note that the permittivities of the respective materials are
not longer the permittivity of free space but include a relative permittivity term,
which explains the electric fields interaction with the material. It is also important to
note that the permittivity in the dielectric is positive, while the permittivity in the
metal is negative. In these equations, we can see that the wave vector term (k1, k2)
perpendicular to the metal / dielectric interface defines the exponential decay of the
fields perpendicular to the interface essentially confining the field to the boundary
of the two materials. Applying continuity of the fields Hy and εEz at the boundary,
and solving for these equations requires that A1 = A2 and
−k2ε2
=k1ε1
(A.7)
This tells us that in order to have a propagating wave at this interface, one of
the materials must have a positive permittivity (dielectric), while the other material
must have a negative permittivity (metal). Furthermore, the magnetic field along the
interface Hy must satisfy Eq. (A.8).
δ2Hy
δz2+ (k0ε0 − β2)Hy = 0 (A.8)
Therefore,
137
k21 = β2 − k2
0ε1 (A.9)
k22 = β2 − k2
0ε2 (A.10)
Combining this result with Eq. (A.7), we arrive at what is known as the ”disper-
sion relation” of the surface plasmon polaritons at the surface of the metal.
β = k0
√ε1ε2
ε1 + ε2(A.11)
Fig. A.2. Surface Plasmon Polaritons (SPPs). Distribution of freecharge carriers oscillating at the metal / dielectric boundary. Thedistribution of the SPP mode can be seen by the red curve.
The material acting as a metal in this case must exhibit a negative permittivity
(ε < 0). This condition is satisfied when the frequency of the incident field is below
the plasma frequency ωp where
ωp =
√ne2
ε0m∗ (A.12)
In Eq. (A.12), n is the number of free electrons in the metal, e is the charge of the
electron, and m∗ is the effective mass of the electron in the metal. To re-emphasize,
a surface wave can only exist in the condition where the permittivity of the metal is
138
negative (εm < 0), and this condition is satisfied at or below the materials plasma
frequency.
A.1 Multilayer Systems and Plasmonic Waveguides
We have solved the wave equation for the case of a single metal / insulator inter-
face, and now move on to look at three-layer systems consisting of metal- insulator-
metal (MIM) and insulator-metal-insulator (IMI) structures. These structures can
be used as plasmonic waveguides guiding this plasmonic mode confined to a sub-
wavelength structure. In the IMI structure, when the thickness of the metal layer
approaches the SPP decay length in the z-direction, a coupled mode will arise be-
tween the two interfaces as shown in Fig. A.3.
Fig. A.3. A coupled SPP mode will exist when the thickness of themetallic layer is below the decay length of the surface mode in an IMIstructure.
This type of symmetric profile of the SPP mode will arise when the dielectrics
have the same positive value of permittivity. These types of IMI structure have
several important features worth noting. First, most of the propagating mode is not
contained in the metal. For this reason, we say that the mode has weak confinement,
and thus has the disadvantage of not being able to be steered well along the metal
139
path. While this structure can be used as a waveguide, if the metal path changes
direction, a large portion of the mode will not be able to follow this new path. Another
disadvantage for such a structure is that in practical applications, it is desirable for
these components to be grouped as densely as possible to fit more components onto
a chip. Having such a mode that is spaced so far into the dielectric region prohibits
such designs, as coupling to adjacent waveguides would typically produce undesirable
results. However, because very little of the mode is contained within the metal, this
type of structure has the advantage of very low losses for this propagating mode.
While the evanescent field suffers no losses in the dielectric material, the permittivity
of metals is a complex value, and must be described as:
ε(ω) = ε′ + iε′′ (A.13)
In Eq. (A.13), ε′ describes the metals susceptibility to polarization, while the term
ε′′ describes losses in the metal. Because very little of the IMI mode is contained in
the metal, it will suffer very little loss. For this reason, modes travelling in such a
structure can propagate for very long distances, and are therefore known as Long
Range Surface Plasmon Polaritons (LRSPP).
As previously mentioned, another type of structure can be used as a waveguide to
propagate such SPPs. An alternative to the IMI structure is the metal-insulator-metal
(MIM) structure shown below in Fig A.4.
Similar to the IMI structure, the MIM structure has a coupled mode between the
two metal interfaces. However, in this case the metal interfaces have an insulating
layer between them. As can be seen in Fig. A.4, most of the field in this MIM
structure is in the metal layers. For this reason, this mode cannot propagate for long
distances, as they suffer from the large losses in the metal. However, this mode is
confined very well, and can thus easily follow the path of the waveguide.
By comparing these two types of waveguide designs, it can be seen that there are
trade-offs to each design. For example, if an optical signal must be sent for a long
distance in a straight line in a system that does not require high component density,
140
Fig. A.4. A coupled SPP mode in a MIM structure. While the modeis confined well, most of the field is in the metal, and will thereforesuffer from the metallic losses.
the IMI structure is the clear choice. Alternatively, if the signal is only required to
travel a short distance in a more dense system, the MIM structure may be the better
choice. However, both structures have the advantage over conventional fiber optics
in that they allow for subwavelength, nanometer confinement of the electromagnetic
fields allowing for plasmonic integration with our current electronics.
A.2 Localized Surface Plasmon Resonance and Nano-Antennas
While the propagating mode of surface plasmon polaritons (SPPs) has been dis-
cussed, there is another type of surface plasmon known as localized surface plasmon
resonance or LSPR. For this case, we consider a structure similar to the the IMI
structure explained in the previous section, however we assume the metal now has a
finite length such as shown below in Fig. A.5.
While in the case of the SPPs propagating on a boundary infinite in length, free
charges were able to move for long distances under the influence of an oscillating field.
However, when the length of this layer becomes finite, we see that under the influence
of an oscillating electromagnetic wave, free charges will build up on the edges of these
141
(a) The basic design of the structure.
(b) The localization of charges due to the finite length of the structure.
Fig. A.5. Geometry of the localized surface plasmon resonance.
conducting metals. The incident electromagnetic wave acts as an Alternating Current
(AC) source, oscillating the free charge carriers at optical frequencies. Naturally,
this type of structure has a resonant frequency at which the metal pairs absorb the
maximum amount of energy and confine it to the gap between metal pairs. For this
reason, this type of structure is known as a nano-antenna and has a wide range of
applications including enhancement of non-linear processes and improvements in solar
cell efficiencies.
A.3 Conclusion
When a wave is incident on a dielectric / metal interface, our boundary conditions
were able to identify the existence of a surface mode known as a surface plasmon
polariton under TM polarization. However, due to losses in the metal to which these
fields are confined, these fields will not propagate for long distances. To exploit
this phenomenon into a practical application (such as a waveguide), the geometry
142
can be configured into an IMI or MIM structure each with its own advantages and
disadvantages. Finally, a similar technique can be used in a non-continuous structure
to create a localized surface plasmon resonance which is a non-propagating mode
but allows for the absorption and confinement of the field to a small volume. This
type of structure can be used as a nano-antenna for various applications requiring
strong field enhancement and confinement. Many of the Equations derived in this
chapter, and structures discussed will have a great amount of application throughout
the remainder of this dissertation.
143
B. GLANCING ANGLE DEPOSITION (GLAD) - NOVEL
APPROACH FOR QUASI 3D FABRICATION
B.1 Glancing Angle Deposition at Purdue
B.1.1 Background
Due to the interest in creating films on non-planar surfaces and non-uniform thick-
nesses, we have ordered a custom designed and built Electron-Beam (e-beam) Evapo-
ration system from PVD Products (Wilmington, MA). The system’s installation was
completed in February 2012, and is located in the cleanroom of the Birck Nanotech-
nology Center. An image of the outside of the system can be seen in Fig. B.1. While
Birck has several other e-beam evaporators, this PVD GLAD system has control over
the substrate’s angle and rotation that make it unique to any of the other evapora-
tion systems on Purdue’s campus. Additionally, the system’s deposition parameters
(deposition rate, thickness) can be programmed to automate the deposition process
for many-layered films.
B.1.2 Hardware
The evaporator has a four-pocket turret, and the deposition angle can be auto-
matically controlled for each pocket. The rotational control of the substrate can be
set to rotate continuously at a designated rate (RPM), or can be set to do a single
angular rotation (e.g. rotate clockwise 90◦) through the computer’s user interface
(discussed later). The valve control for loading/unloading the chamber are all man-
ually controlled and are located on the left side of the evaporation chamber (shown
in Fig. B.1). Base pressures of 5 × 10−6 can be reached in approximately 1 hour,
144
while pressures of 2 × 10−8 Torr can be achieved by letting the cryo pump run for
approximately 24 hours.
Fig. B.1. Some of the external components of the GLAD system
The inside of the evaporation chamber can be seen in Fig. B.2. While most of
the internal components are standard to most e-beam evaporators, the sample holder
and quartz crystal monitors (QCM) are slightly modified at should be explained in
detail. The sample holder’s angle can be controlled via the computer’s user interface
(discussed later). The motor for the angular control of the substrate is located out-
side the chamber, as seen in Fig. B.1, while the motor for the sample’s rotational
control is located internally. One of the design requirements of the GLAD system
was the capability to deposit large amounts of material in a single deposition without
breaking vacuum, and the system was designed accordingly. First, pockets for very
large (30cc) crucibles were included to accommodate the large volume of deposited
material. Secondly, because QCMs are extremely sensitive to (and deteriorate with)
the amount of deposited mass, the system has two separate QCMs with independent
shutters that can be opened and closed when one QCM has deteriorated. These in-
145
ternal components allow for long depositions of thick and multi-layered films without
breaking vacuum.
Fig. B.2. Some of the internal components of the GLAD system
The current materials in the chamber, and their respective pocket numbers are
listed below:
1. Germanium (Ge)
2. Silver (Ag)
3. Silicon Dioxide (SiO2)
Other materials that can be evaporated in the chamber (though they are not
loaded) include but are not limited to:
146
• Aluminum (Al)
• Aluminum Oxide (Al2O3)
• Gold (Au)
• Chromium (Cr)
• Silicon (Si)
• Copper (Cu)
• Titanium Dioxide (TiO2)
• Iron (Fe)
B.1.3 Automation and Computer User Interface
In order to automate the deposition of thick and multi-layered films, as well as
the sample’s angle and rotation, many of the system’s controls can be manipulated
through an external computer. Physically located next to the evaporation chamber,
a laptop controls the sample’s motion through a Graphical User Interface (GUI),
programmed in LabView. A screenshot of this GUI, along with important controls
are shown in Fig. B.3.
The bottom left box A: “Rotation Control” controls the substrates rotation. There
are two basic methods of oration: 1) continuously rotating at a specified rate (RPM),
or 2) rotating by an exact amount (e.g. 90◦) and stopping. The rotation is done
by a stepper motor, where full 360◦ rotation requires 20,000 steps. Therefore, 180◦
rotation is 10,000 steps and so forth.
The system has a 4-pocket turret, where the angle of deposition for each pocket can
be independently controlled. The designated angle foe each pocket is input into box
B: “Angle Control”. The angles are input as degrees (not radians), and are applied
to the substrate when the “Set Index Positions” button is clicked. The angle of the
substrate will change only when the source material in the corresponding pocket is
being evaporated.
147
Because the system is designed to evaporate very thick (microns) and multilayer
films, the computer can save critical system information throughout the entire de-
position process. This information includes chamber pressure, deposition rate, film
thickness, substrate angle rotation, and so on. This data is saved in a plan-text comma
separated value (CSV) format, and its collection time interval can be assigned in Box
C: “System Data Collection”. More detailed instructions on loading/unloading the
chamber can be found in Appendix C.1 “Loading and Unloading the GLAD Cham-
ber”
B.1.4 WORDS OF CAUTION
The systems’ automation is a wonderful and essential feature for fabricating thick
and many-layered structures. Depositing many-layered films can take very long
amounts of time (some of the structures fabricated in this dissertation have taken
in excess of 24 hours to deposit). Automating this process allows the machine to
continue deposition without input from the user. However, this feature can lie users
into a false sense of security, so words of caution should be considered.
Although unlikely, there are several possible problems that can arise which could
lead to catastrophic system failure and destruction. A magnet failure is unlikely but
unpredictable. In the case of this event, the high-powered electron beam will go off
in an arbitrary direction, and can burn or melt through whatever it comes in contact.
This could burn a hole in the chamber itself and/or damage any internal components
in quite a short time period. The only way to catch this problem is to be present
and observant during deposition. Another possible (though avoidable) problem that
could arise is burning through a crucible and turret with the e-beam. This potential
problem is espycially apparent with dielectric materials, as they do not “pool” like
metals. This problem can be avoided by making sure the crucibles are always full,
and using proper sweeping.
148
Fig. B.3. Screenshot of the GUI for the GLAD system.
149
C. STEP-BY-STEP INSTRUCTIONS FOR OPERATING
GLAD
C.1 Loading and Unloading the GLAD Chamber
1. Turn off ion gauge and wait 2 minutes for it to cool
2. Close the gate valve fully
3. Open the vent valve, wait for pressure to reach 760 Torr
4. The chamber door is difficult to open. Either wait a while (∼ 10 minutes) then
open the door, or pull VERY hard on the door to open.
5. While the chamber is open, double glove and check the turret pockets have
sufficientt material, chamber is clean, Quartz Crystal Monitors are in good health
(above ∼80%)
6. The sample holder is friction-mounted in the chamber. There are two Allen
wrenches on top of the chamber. Use the larger wrench to loosen the 2 screws
while holding the sample holder with the other hand. Be careful not to drop the
sample holder! I find the whole process is easier when the holder is rotated to
45◦.
7. Mount the sample into the sample holder using the smaller Allen wrench. Tip:
think ahead of time about where the shadow from the sample clips will fall -
especially at clanking angles (as it will cast a long shadow).
8. Remount the sample holder as before. Be sure it is tightly secured before releas-
ing with your hand - as to not let it fall down. Shake the sample holder slightly
so as to make sure it is securely mounted and will not fall down on its own.
Again, make note of the orientation of the sample and consider any shadowing
from the mounting clips.
150
9. Close the chamber, tighten acre-mount on the side of the chamber (to make a
tight seal).
10. Close the vent valve
11. Open the roughing valve, wait for pressure to drop down to below 250mTorr
(0.250) Torr
12. Close the roughing valve
13. SLOWLY open the gate valve. Once the pressure begins to drop, wait 1 minute,
then continue opening the valve slowly. Once the pressure is below ∼1e−4 Torr,
open the valve up all the way and let the system pump down.
14. Wait ∼5 minutes to let the system drop in pressure.
15. Turn on the ion gauge, record the pressure in the logbook
16. Wait ∼1 hour for the pressure to drop to 5e−6 Torr
17. Wait ∼24 hours for the pressure to drop to 5e−8 Torr
C.2 Running an Evaporation
1. Turn on High Voltage switch and controller switch (bottom left - below the
chamber)
2. Turn on the “Sweep Controller” switch
3. Turn on the “Evap Enable” switch and wait for ∼2 minutes for the light to stop
blinking.
4. On the Inficon thin film deposition controller, go into the process menu to select
and edit a recipe. Here, film layers can be added or removed and parameters
(such as film thickness and deposition rate) can be modified.
5. Go back to the main menu, be sure the correct recipe has been selected.
6. Start the process.
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7. The sample angle for the 4 crucibles can be input into the “Index Positions” box
on the computer.
8. When the process finishes, turn the system off in the reverse order: evap enable,
sweep controller, high voltage, and controller.
9. Make sure the ion gauge is turned off and wait 2 minutes for it to cool before
venting.
C.3 Other Notes and Comments
• Get all source materials from the BNC staff (namely Dave Lubelski or Kenny
Schwartz)
• The “chimney” will need to be cleaned periodically, as pieces of deposited ma-
terial will flake off. Take the chimney out and scrape it with a razor blade. If
further cleaning is needed, Dave Lubelski can clean it with a sandblaster.
• Clean and vacuum any material that has fallen in the chamber - especially if it
is near any source crucibles.
• Keep the chamber clean! Ask BNC staff before putting any new materials inside
the chamber.
• We installed a plastic shield on the outside of the chamber around the substrate
angle rotation motor. This is there for safety and should never be removed. it
is a “pinch-point” and can crush a person’s fingers.
• Never open any of the High-Voltage boxes - they are an electric hazard and can
be lethal
VITA
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VITA
Paul R. West currently works for Intel Semiconductor Manufacturing Company
- Portland Technology Development as a Defect Metrology Yield Engineer in Hills-
boro, Oregon. He specializes in the design and fabrication of optical materials, with
emphasis on detecting and imaging of subwavelength objects. He graduated with a
B.S.E.E. from Michigan Technological University in 2008, and Ph.D. from Purdue
University in 2014. His primary advisors at Purdue are Dr. Alexandra E. Boltasseva
and Dr. Vladimir M. Shalaev.